Answer:
The least possible price is p = £110
Step-by-step explanation:
From the question we are told that
The number of bracelets to be made is [tex]n = 150[/tex]
The length of silver require for on bracelet is [tex]x = 26 \ cm = 0.26 \ m[/tex]
The option of silver length packs that she buys is a = 10.5 m packs
b = 3.7 m packs
Generally
1 bracelet [tex]\to[/tex] 0.26 m
150 bracelet [tex]\to[/tex] z
=> [tex]z = \frac{150 * 0.26}{1}[/tex]
=> [tex]z = 39 \ m[/tex]
Now for option a i.e 10.5 m per pack
The number of packs require is
[tex]v = \frac{z}{a}[/tex]
=> [tex]v = \frac{39}{ 10.5}[/tex]
=> [tex]v = 3.7 1[/tex]
given that the number of packs cannot be a fraction but an integer hence she needs to purchase v = 4
and that 4 packs would equal t = 4 * 10.5 = 42 meters of silver
Now for option d i.e 3.7 meters per pack
The number of packs requires is
[tex]w = \frac{z}{b}[/tex]
=> [tex]w = \frac{39}{3.7}[/tex]
=> [tex]w = 10.54[/tex]
given that the number of packs cannot be a fraction but an integer hence she needs to purchase w= 11
and that 11 packs would equal t = 11 * 3.7 = 40.7 meters of silver
So the comparing the option and option b we see that for her to pay as little as possible she needs to go for option b since option be will produce the 150 bracelet with a little excess while option a will produce the 150 bracelet with much excess
Assuming the price for the 3.7 m pack is £10
And the price for the 10.7 pack is £30
The least possible amount she would pay is
[tex]p = 10 * 11[/tex]
p = £110
Repeated-measures and matched-subjects experiments Aa Aa Repeated-measures experiments measure the same set of research participants two or more times, while matched-subjects experiments study participants who are matched on one or more characteristics. Which of the following are true for both a repeated-measures experiment and a matched-subjects experiment when used to compare two treatment conditions? Check all that apply.
A. The researcher computes difference scores to compute a t statistic
B. If the researcher has n number of participants to use in the experiment, then the degrees of freedom will be the same in a repeated-measures experiment or in a matched-subjects experiment
C. The researcher must compute an estimated standard error for the mean difference score to compute a t statistic.
D. Participants in both types of experiments are all measured the same number of times
A matched-subjects experiment produced a t statistic with a df of 9. How many subjects participated in this study?
A. 20
B. 10
C. 18
D. 9
For a repeated-measures experiment comparing two treatment conditions, the t statistic has a df of 11. How many subjects participated in this study?
A. 12
B. 22
C. 24
D. 11
Answer:
1. C. The researcher must compute an estimated standard error for the mean difference score to compute a t statistics.
2. B. 10
3. A. 12
Step-by-step explanation:
The degrees of freedom is number of independent variable factors that affect the range of parameters. The degrees of freedom is the calculation of number values that are free to vary. The degrees of freedom is calculated by N-1. Standard error is the estimated deviation of standard deviation from its sample mean distribution.
Suppose you were exploring the hypothesis that there is a relationship between parents’ and children’s party identification. Would we be correct in inferring that such a relationship also exists in the population? Explain your answer. What is the probability that any relationship we found is due to pure chance?
Answer:
No
It could be purely due to chance.
Step-by-step explanation:
A population is defined as the whole group which has the same characteristics. For example a population of the college belongs to the same college . But a sample may be an element of a population.
So it is not necessary for a population to have the same characteristics as the sample.
But it is essential for the sample to have at least one same characteristics as the population.
So we would not be correct in inferring that such a relationship also exists in the population.
It is a hypothesis which can be true or false due to certain conditions or limitations as the case maybe.
For example in a population of smokers some may be in the habit of taking cocaine. But a sample of cocaine users does not mean the whole population uses it.
It could be purely due to chance if we find out that there is a relationship between parents’ and children’s party identification in the population.
Transform the given parametric equations into rectangular form. Then identify the conic. x= 5cos(t) y= 2sin(t)
Answer:
Solution : Option D
Step-by-step explanation:
The first thing we want to do here is isolate the cos(t) and sin(t) for both the equations --- ( 1 )
x = 5cos(t) ⇒ x / 5 = cos(t)
y = 2sin(t) ⇒ y / 2 = sin(t)
Let's square both equations now. Remember that cos²t + sin²t = 1. Therefore, we can now add both equations after squaring them --- ( 2 )
( x / 5 )² = cos²(t)
+ ( y / 2 )² = sin²(t)
_____________
x² / 25 + y² / 4 = 1
Remember that addition indicates that the conic will be an ellipse. Therefore your solution is option d.
A box is dragged across 20 meters with a force of 60 Newtons, which are kg*m/s^2
Answer:
Mass= 6kg
Acceleration= 10 ms^-2
Work done = 1200Nm
Step-by-step explanation:
kg*m/s^2 represent the force.
The kg represent the mass
The m/s^2 represent the acceleration
The acceleration here will be due to gravity force= 10 ms^-2
Then the mass= 60/10
Mass= 6 kg
The force = 60 Newton
Distance covered in the direction of the the force= 20 Meters
The work done in the direction of the force= force* distance
The work done in the direction of the force=60*20
The work done in the direction of the force=1200 Nm
Answer: 20 • 60
Step-by-step explanation:
How to find which ratio is largest
Find the total amount in the compound interest account.
$10000 is compounded semiannually at a rate of 9% for 22 years.
(Round to the nearest cent.)
Answer:
$69,361.23
Step-by-step explanation:
[tex] A = P(1 + \dfrac{r}{n})^{nt} [/tex]
[tex] A = 10000(1 + \dfrac{0.09}{2})^{2 \times 22} [/tex]
[tex]A = 10000(1.045)^{44}[/tex]
[tex] A = 69361.23 [/tex]
Answer: $69,361.23
A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 19 phones from the manufacturer had a mean range of 1160 feet with a standard deviation of 32 feet. A sample of 11 similar phones from its competitor had a mean range of 1130 feet with a standard deviation of 30 feet.
Required:
Do the results support the manufacturer's claim?
Complete question is;
A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 19 phones from the manufacturer had a mean range of 1160 feet with a standard deviation of 32 feet. A sample of 11 similar phones from its competitor had a mean range of 1130 feet with a standard deviation of 30 feet. Required:
Do the results support the manufacturer's claim?
Let μ1 be the true mean range of the manufacturer's cordless telephone and μ2 be the true mean range of the competitor's cordless telephone. Use a significance level of α = 0.01 for the test. Assume that the population variances are equal and that the two populations are normally distributed
Answer:
We will fail to reject the null hypothesis as there is no sufficient evidence to support the manufacturers claim.
Step-by-step explanation:
For the first sample, we have;
Mean; x'1 = 1160 ft
standard deviation; σ1 = 32 feet
Sample size; n1 = 19
For the second sample, we have;
Mean; x'2 = 1130 ft
Standard deviation; σ2 = 30 ft
Sample size; n2 = 11
The hypotheses are;
Null Hypothesis; H0; μ1 = μ2
Alternative hypothesis; Ha; μ1 > μ2
The test statistic formula for this is;
z = (x'1 - x'2)/√[(σ1)²/n1) + (σ2)²/n2)]
Plugging in the relevant values, we have;
z = (1160 - 1130)/√[(32)²/19) + (30)²/11)]
z = 2.58
From the z-table attached, we have a p-value = 0.99506
This p-value is more than the significance value of 0.01,thus,we will fail to reject the null hypothesis as there is no sufficient evidence to support the manufacturers claim.
NEED HELP ASAP!! Angles of Elevation and Despression! Need to find y! Round to the nearest tenth!!
Answer:
y = 178.3 ftStep-by-step explanation:
Since the above figure is a right angled triangle we can use trigonometric ratios to find y
To find y we use tan
tan∅ = opposite/ adjacent
From the question
the opposite is y
the adjacent is 350 ft
Substitute the values into the above formula
That's
[tex] \tan(27) = \frac{y}{350} [/tex]
y = 350 tan 27
y = 178.3339
We have the final answer as
y = 178.3 ft to the nearest tenthHope this helps you
Identify whether the sampling method is simple random, systematic, stratified, cluster, or convenience. Explain.
In a nationwide study of registered voters conducted by The New York Times, 390 people are randomly selected out of those registered as Republicans, 430 people are randomly selected out of those registered as Democrats, and 180 people are randomly selected out of those registered as Independents.
Answer: stratified
Step-by-step explanation:
In stratified sampling, you divide the population into subgroups, or strata, with similar characteristics, like here we have divided the population into subgroups that depend on their political alignment. This is used when you can expect that the results have a noticeable variation between the different subgroups. Usually, you want to have the same number of population for eac subgroup, but sometimes it is hard for different reasons (not enough people in one subgroup, for example)
In cluster sampling we also use subgroups, but the subgroup itself is the unit of the sampling, while in this case, we are randomly selecting individuals of the given subgroups.
So this would be a "stratified sampling".
3x18 = 3 (10+8) is an example of the _________ property of multiplication.
Answer:
3x18 = 3 (10+8) is an example of the commutative property of multiplication
Step-by-step explanation:
Answer: commutative property of multiplication
Step-by-step explanation:
how many meters are in 250 centimeters
Answer:
2.5 meters
Step-by-step explanation:
What is the x-coordinate of the point shown in the graph?
______
Answer:
Hey there!
The x coordinate would be -5.
Let me know if this helps :)
As we can see in the Graph,
x-coordinate = - 5y-coordinate = - 7
The manager of a garden shop mixes grass seed that is 60% rye grass with 140 pound of grass seed that is 80% rye grass to make a mixture that is 74% rye grass. How much of the 60% mixture is used?
Answer:
60 pounds
Step-by-step explanation:
Let x = number of pounds of grass seeds A
The number of pounds of grass seed B = 140 pounds
Total pounds of the resulting mixture = (140 + x) pounds
Rye grass A = 60% = 0.6
Rye grass B = 80% = 0.8
Total percent of mixture formed = 74% = 0.74
Hence, we have the equation:
0.6x + 0.8 × 140 = 0.74 ( 140 + x)
0.6x + 112 = 103.6 + 0.74x
Collect like terms
112 - 103.6 = 0.74x - 0.6x
8.4 = 0.14x
x = 60 pounds
Therefore, the quantity of the 60% mixture used is 60 pounds.
The manager of a garden shop mixes grass seed that is 60% rye grass with 140 pound of grass seed that is 80% rye grass to make a mixture that is 74% rye grass. How much of the 60% mixture is used?
For the following polynomial, find P(a), P(-x) and P(x + h).
P(x) = 7x-6
Answer:
Step-by-step explanation:
Hello, please consider the following.
P(a) = 7 * a - 6
P(-x)= 7 *(-x) - 6 = -7x - 6
P(x+h) = 7 * (x+h) - 6 = 7x + 7h - 6
Hope this helps.
Thank you.
The values of the polynomial for the given expressions are:
P(a) = 7a - 6
P(-x) = -7x - 6
P(x + h) = 7x + 7h - 6
To find P(a), P(-x), and P(x + h) for the given polynomial P(x) = 7x - 6, we need to substitute the respective values of x into the polynomial expression.
1. P(a):
P(a) = 7a - 6
2. P(-x):
P(-x) = 7(-x) - 6
P(-x) = -7x - 6
3. P(x + h):
P(x + h) = 7(x + h) - 6
P(x + h) = 7x + 7h - 6
To know more about polynomial:
https://brainly.com/question/2928026
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Marco purchased a large box of comic books for $300. He gave 15 of the comic books to his brother and then sold the rest on an internet website for $330 making a profit , making a profit of $1.50 on each one.how many comic books were in the box? what was the original price of each comic book (assuming they all cost the same amount)?
Answer: There are 75 books.
Price of each book = $4.
Step-by-step explanation:
Let x = Number of books in the box.
Then as per given,
Cost of x books = $300
Cost of one book = [tex]\$(\dfrac{300}x)[/tex]
Books left after giving 15 of them = x-15
Selling price of (x-15) books= $330
Selling price of one book = [tex]\$(\dfrac{330}{x-15})[/tex]
Profit on each book= $1.50
Profit = selling price - cost price
[tex]\Rightarrow 1.50=\dfrac{330}{x-15}-\dfrac{300}{x}\\\\\Rightarrow\ 1.50=\dfrac{330(x)-300(x-15)}{x(x-15)}\\\\\Rightarrow\ 1.50=\dfrac{330x-300x+4500}{x^2-15x}\\\\\Rightarrow\ 1.50(x^2-15x)=30x+4500\\\\\Rightarrow\ 1.50x^2-22.5x=30x+4500\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ 1.50x^2-52.5x-4500=0\\\\\Rightarrow\ x^2-25x-3000=0\ \ [\text{divide by 1.5}][/tex]
[tex]\Rightarrow (x+40)(x-75)=0\\\\\Rightarrow\ x=-40,75[/tex]
Number of books cannot be negative.
So, there are 75 books.
Price of each book = [tex]\dfrac{300}{75}=\$4[/tex]
So price of each book = $4.
A random sample of 1400 Internet users was selected from the records of a large Internet provider and asked whether they would use the Internet or the library to obtain information about health issues. Of these, 872 said they would use the Internet
1. The standard error ˆp SE of the proportion pˆ that would use the Internet rather than the library is:_______
a. 0.013.
b. 0.25.
c. 0.485.
d. 0.623.
2. If the Internet provider wanted an estimate of the proportion p that would use the Internet rather than the library, with a margin of error of at most 0.02 in a 99% confidence interval, how large a sample size would be required? (Assume that we don’t have any prior information about p).
a. 33
b. 3909
c. 2401
d. 4161
Answer:
1 [tex]\sigma_{\= x } = 0.0130[/tex]
2 [tex]n = 3908.5[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n_p = 1400[/tex]
The number of those that said the would use internet is [tex]k = 872[/tex]
The margin of error is [tex]E = 0.02[/tex]
Generally the sample proportion is mathematically evaluated as
[tex]\r p = \frac{k}{n_p}[/tex]
substituting values
[tex]\r p = \frac{ 872}{1400}[/tex]
substituting values
[tex]\r p = 0.623[/tex]
Generally the standard error of [tex]\r p[/tex] is mathematically evaluated as
[tex]\sigma_{\= x } = \sqrt{\frac{\r p (1- \r p)}{n} }[/tex]
substituting values
[tex]\sigma_{\= x } = \sqrt{\frac{0.623 (1- 0.623)}{1400} }[/tex]
[tex]\sigma_{\= x } = 0.0130[/tex]
For a 95% confidence interval the confidence level is 95%
Given that the confidence interval is 95% the we can evaluated the level of confidence as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1\%[/tex]
[tex]\alpha = 0.01[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from normal distribution table (reference math dot armstrong dot edu) , the value is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
Give that the population size is very large the sample size is mathematically represented as
[tex]n = [ \frac{Z_{\frac{\alpha }{2} ^2 * \r p ( 1 - \r p )}}{E^2} ][/tex]
substituting values
[tex]n = [ \frac{2.58 ^2 * 0.623 ( 1 -0.623 )}{0.02^2} ][/tex]
[tex]n = 3908.5[/tex]
If vectors i+j+2k, i+pj+5k and 5i+3j+4k are linearly dependent, the value of p is what?
Answer:
[tex]p = 2[/tex] if given vectors must be linearly independent.
Step-by-step explanation:
A linear combination is linearly dependent if and only if there is at least one coefficient equal to zero. If [tex]\vec u = (1,1,2)[/tex], [tex]\vec v = (1,p,5)[/tex] and [tex]\vec w = (5,3,4)[/tex], the linear combination is:
[tex]\alpha_{1}\cdot (1,1,2)+\alpha_{2}\cdot (1,p,5)+\alpha_{3}\cdot (5,3,4) =(0,0,0)[/tex]
In other words, the following system of equations must be satisfied:
[tex]\alpha_{1}+\alpha_{2}+5\cdot \alpha_{3}=0[/tex] (Eq. 1)
[tex]\alpha_{1}+p\cdot \alpha_{2}+3\cdot \alpha_{3}=0[/tex] (Eq. 2)
[tex]2\cdot \alpha_{1}+5\cdot \alpha_{2}+4\cdot \alpha_{3}=0[/tex] (Eq. 3)
By Eq. 1:
[tex]\alpha_{1} = -\alpha_{2}-5\cdot \alpha_{3}[/tex]
Eq. 1 in Eqs. 2-3:
[tex]-\alpha_{2}-5\cdot \alpha_{3}+p\cdot \alpha_{2}+3\cdot \alpha_{3}=0[/tex]
[tex]-2\cdot \alpha_{2}-10\cdot \alpha_{3}+5\cdot \alpha_{2}+4\cdot \alpha_{3}=0[/tex]
[tex](p-1)\cdot \alpha_{2}-2\cdot \alpha_{3}=0[/tex] (Eq. 2b)
[tex]3\cdot \alpha_{2}-6\cdot \alpha_{3} = 0[/tex] (Eq. 3b)
By Eq. 3b:
[tex]\alpha_{3} = \frac{1}{2}\cdot \alpha_{2}[/tex]
Eq. 3b in Eq. 2b:
[tex](p-2)\cdot \alpha_{2} = 0[/tex]
If [tex]p = 2[/tex] if given vectors must be linearly independent.
If the solutions for a quadratic equation are -2 and 5 what is the equation
Answer:
f(x) = x^2 - 3x -10
Step-by-step explanation:
If the solutions are {-2, 5}, the factors of the quadratic are (x + 2) and (x - 5).
The equation is f(x) = (x + 2)(x - 5) = x^2 - 3x -10
Write 8x8x88888 as power
Answer:
8[2]×88888
Step-by-step explanation:
[8×8]=8[2]×88888
a sheet metal worker earns $26.80 per hour after receiving a 4.5% raise. what was the sheet metal worker's hourly pay before raise? Round your answer to the nearest cent
Answer
$25.59
Step-by-step explanation:
subtract by percentage or you can also do:
100% - 4.5% = 95.5%
95.5% x $26.80 = $25.594
IF ROUNDED: $25.59
Answer:
$25.65
Step-by-step explanation:
Let the original hourly rate be r.
Then 1.045r + $26.80/hr.
Dividing both sides by 1.045, we get:
$26.80/hr
r = ------------------ = $25.65 This was the before-raise pay rate.
1.045
Need help with this as soon as possible pls
Answer:
i think
x=6.77
y=11.33
These figures are similar. The area of one is given. Find the area of the other. PLZ HELP
Answer: 6
Step-by-step explanation:
Shyla's research shows that 8 empty cans make 1/4 pound of aluminum. Shyla wants to know how many cans does it take to make 5 pounds of aluminum. How many cans are there per pound of aluminum?
Answer:
They will need 160 cans to make 5 lbs
32 cans for 1 lbs
Step-by-step explanation:
We can use ratios to solve
8 cans x cans
--------------- = ---------------
1/4 lbs 5 lbs
Using cross products
8 * 5 = 1/4x
40 = 1/4 x
Multiply each side by 4
4 * 40 = 1/4 x * 4
160 =x
They will need 160 cans to make 5 lbs
8 cans x cans
--------------- = ---------------
1/4 lbs 1 lbs
Using cross products
8 * 1 = 1/4x
Multiply each side by 4
8*4 = x
32 cans for 1 lbs
Answer:
32 cans per pound of aluminum
160 cans per 5 pounds of aluminum
Step-by-step explanation:
will make it short and simple.
8 empty cans can make 1/4 pound of aluminum.
therefore... 8 x 4 = 32 cans per pound of aluminum.
Number of cans to make 5 pounds of aluminum = 32 x 5
= 160 cans per 5 pounds of aluminum
Shane biked 1 mile less than three times the number of miles Lissette biked. Shane biked a total of 7 miles. Write an equation to determine how many miles Lissette biked.
Answer:
2.67 miles (or 8/3 miles which is also 3 2/3 miles)
Step-by-step explanation:
S (shane) = 7
L (lissette) = ??
S = 3(L) - 1
7 = 3L - 1
8 = 3L
L = 2.67 miles
What is the difference between congurent and similar ?
Answer:
When a shape is congruent they are equal in shape, size, and measure. Although if a shape is similar they will be the same shape, but not the same size, instead they will be proportionate.
Step-by-step explanation:
Answer:
CongruentCongruent figures are identical in size, shape and measure. SimilarTwo figures are similar if they have the same shape, but not necessarily the same size.
Step-by-step explanation:
Find the surface area of the solid given the net.
Answer:
288
Step-by-step explanation:
Area of two triangles=2(½bh)
=bh
=8×6
=48
For the rectangles=lb + lb +lb
l(b+b+b)
=12(8+6+6)
=12×20
=240
Total area=240 +48=288
Question: The hypotenuse of a right triangle has a length of 14 units and a side that is 9 units long. Which equation can be used to find the length of the remaining side?
Answer:
The hypotenuse is the longest side in a triangle.
a^2=b^2+c^2.
14^2=9^2+c^2.
c^2=196-81.
c^2=115.
c=√115.
c=10.72~11cm
Heights of men on a baseball team have a bell-shaped distribution with a mean of and a standard deviation of . Using the empirical rule, what is the approximate percentage of the men between the following values? a.166 cm and 202 cm b. 172cm and 196cm
Let assume that the mean is 184 and the standard deviation is 6
Heights of men on a baseball team have a bell-shaped distribution with a mean 184 of and a standard deviation of 6 . Using the empirical rule, what is the approximate percentage of the men between the following values? a.166 cm and 202 cm b. 172 cm and 196cm
Answer:
P(156<X<202) = 99.7%
P(172<X<196) = 95.5%
Step-by-step explanation:
Given that :
Heights of men on a baseball team have a bell-shaped distribution with a mean of and a standard deviation of . Using the empirical rule, what is the approximate percentage of the men between the following values? a.166 cm and 202 cm b. 172 cm and 196cm
For a.
Using the empirical rule, what is the approximate percentage of the men between the following values 166 cm and 202 cm.
the z score can be determined by using the formula:
[tex]z = \dfrac{X - \mu}{\sigma}[/tex]
[tex]z(166) = \dfrac{166-184}{6}[/tex]
[tex]z(166) = \dfrac{-18}{6}[/tex]
z(166) = -3
[tex]z(202) = \dfrac{202-184}{6}[/tex]
[tex]z(202) = \dfrac{18}{6}[/tex]
z(202) = 3
P(156<X<202) = P( μ - 3σ < X < μ + 3σ )
P(156<X<202) = P( - 3 < Z < 3)
P(156<X<202) = P( Z < 3) - P(Z < -3)
P(156<X<202) = 0.99865- 0.001349
P(156<X<202) = 0.997301
P(156<X<202) = 99.7%
For b.
b. 172 cm and 196cm
[tex]z = \dfrac{X - \mu}{\sigma}[/tex]
[tex]z(172) = \dfrac{172-184}{6}[/tex]
[tex]z(172) = \dfrac{-12}{6}[/tex]
z(172) = -2
[tex]z(196) = \dfrac{196-184}{6}[/tex]
[tex]z(196) = \dfrac{12}{6}[/tex]
z(196) = 2
P(172<X<196) = P( μ - 2σ < X < μ + 2σ )
P(172<X<196) = P( - 2 < Z < 2)
P(172<X<196) = P( Z < 2) - P(Z < -2)
P(172<X<196) = 0.9772 - 0.02275
P(172<X<196) = 0.95445
P(172<X<196) = 95.5%
Each of three identical jewelry boxes has two drawers. Each drawer of the first box contains a gold coin. Each drawer of the second box contains a silver coin. In the third box, one drawer has a gold coin and the other drawer a silver coin. If a box and drawer are selected at random, and the selected drawer has a silver coin, what is the probability that the other drawer has a gold coin
Answer:
75%
Step-by-step explanation:
75% of possibility to have gold coin
The Bay Area Online Institute (BAOI) has set a guideline of 60 hours for the time it should take to complete an independent study course. To see if the guideline needs to be changed and if the actual time taken to complete the course exceeds60 hours, 16 students are randomly chosen and the average time to complete the course was 68hours with a standard deviation of 20 hours. What inference can BAOI make about the time it takes to complete this course?
Answer:
At the 5% level, BAOI can infer that the average time to complete does not exceeds 60 hours.
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 60 \ hr[/tex]
The sample size is [tex]n = 16[/tex]
The sample mean is [tex]\= x = 68 \ hr[/tex]
The standard deviation is [tex]\sigma = 20 \ hr[/tex]
The null hypothesis is [tex]H_o : \mu = 60[/tex]
The alternative [tex]H_a : \mu > 60[/tex]
Here we would assume the level of significance of this test to be
[tex]\alpha = 5\% = 0.05[/tex]
Next we will obtain the critical value of the level of significance from the normal distribution table, the value is [tex]Z_{0.05} = 1.645[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \= x - \mu}{ \frac{ \sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{ 68 - 60 }{ \frac{ 20 }{\sqrt{16} } }[/tex]
[tex]t = 1.6[/tex]
Looking at the value of t and [tex]Z_{\alpha }[/tex] we see that [tex]t< Z_{\alpha }[/tex] hence we fail to reject the null hypothesis
This means that there no sufficient evidence to conclude that it takes more than 60 hours to complete the course
So
At the 5% level, BAOI can infer that the average time to complete does not exceeds 60 hours.
