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# Hypothesis Testing 20 questions

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Question 1 of 20 1.0 Points
Results from previous studies showed 79% of all high school seniors from a certain city plan to attend college after graduation. A random sample of 200 high school seniors from this city reveals that 162 plan to attend college. Does this indicate that the percentage has increased from that of previous studies? Test at the 5% level of significance.

Compute the z or t value of the sample test statistic.

A.t = 1.645
B.z = 1.96
C.z = 0.69
D.z = 0.62

Question 2 of 20
In an article appearing in Today's Health a writer states that the average number of calories in a serving of popcorn is 75. To determine if the average number of calories in a serving of popcorn is different from 75, a nutritionist selected a random sample of 20 servings of popcorn and computed the sample mean number of calories per serving to be 78 with a sample standard deviation of 7.

State the null and alternative hypotheses.

A.H0: = 75, H1: ≠ 75
B.H0: 75, H1: < 75
C.H0: = 75, H1: > 75
D.H0: 75, H1: > 75

Question 3 of 20 1.0 Points
A null hypothesis can only be rejected at the 5% significance level if and only if:

A.a 95% confidence interval does not include the hypothesized value of the parameter
B.a 95% confidence interval includes the hypothesized value of the parameter
C.the null hypotheses includes sampling error
D.the null hypothesis is biased

Question 4 of 20
If a teacher is trying to prove that a new method of teaching economics is more effective than a traditional one, he/she will conduct a:

A.confidence interval
B.two-tailed test
C.one-tailed test
D.point estimate of the population parameter

Question 5 of 20 1.0 Points
Smaller p-values indicate more evidence in support of the:

A.alternative hypothesis
B.quality of the researcher
C.null hypothesis
D.the reduction of variance

Question 6 of 20 1.0 Points
A manufacturer of flashlight batteries took a sample of 13 batteries from a day's production and used them continuously until they failed to work. The life lengths of the batteries, in hours, until they failed were: 342, 426, 317, 545, 264, 451, 1049, 631, 512, 266, 492, 562, and 298.

At the .05 level of significance, is there evidence to suggest that the mean life length of the batteries produced by this manufacturer is more than 400 hours?

A.No, because the test value 1.257 is greater than the critical value 1.115
B.No, because the p-value for this test is equal to .1164
C.Yes, because the test value 1.257 is less than the critical value 2.179
D.Yes, because the test value 1.257 is less than the critical value 1.782

Question 7 of 20 1.0 Points
The "Pizza Hot" manager commits a Type I error if he/she is

A.switching to new style when it is no better than old style
B.switching to new style when it is better than old style
C.staying with old style when new style is better
D.staying with old style when new style is no better than old style

Question 8 of 20 1.0 Points
You conduct a hypothesis test and you observe values for the sample mean and sample standard deviation when n = 25 that do not lead to the rejection of H0. You calculate a p-value of 0.0667. What will happen to the p-value if you observe the same sample mean and standard deviation for a sample size larger than 25?

A.The p - value increases
B.The p - value may increase or decrease
C.The p - value stays the same
D.The p - value decreases

Question 9 of 20 1.0 Points
Suppose that the mean time for a certain car to go from 0 to 60 miles per hour was 7.7 seconds. Suppose that you want to test the claim that the average time to accelerate from 0 to 60 miles per hour is longer than 7.7 seconds. What would you use for the alternative hypothesis?

A.H1: 7.7 seconds
B.H1: = 7.7 seconds
C.H1: > 7.7 seconds
D.H1: < 7.7 seconds

Question 10 of 20 1.0 Points
Results from previous studies showed 79% of all high school seniors from a certain city plan to attend college after graduation. A random sample of 200 high school seniors from this city reveals that 162 plan to attend college. Does this indicate that the percentage has increased from that of previous studies? Test at the 5% level of significance.

State the null and alternative hypotheses.

A.H0: m = .79, H1: m > .79
B.
H0: = .79, H1: > .79
C.H0: p = .79, H1: p ≠ .79
D.H0: p ≤ .79, H1: p > .79

Question 11 of 20 1.0 Points
The form of the alternative hypothesis can be:

A.one or two-tailed
B.neither one nor two-tailed
C.two-tailed
D.one-tailed

Question 12 of 20
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Suppose a firm that produces light bulbs wants to know whether it can say that its light bulbs typically last more than 1500 hours. Hoping to find support for their claim, the firm collects a random sample of n = 25 light bulbs and records the lifetime (in hours) of each bulb. The information related to the hypothesis test is presented below.

Test of H0: 1500 versus H1: > 1500
Sample mean 1509.5
Sample standard deviation 24.27

Assuming the life length of this type of lightbulb is normally distributed, if you wish to conduct this test using a .05 level of significance, what is the critical value that you should use? Place your answer, rounded to 3 decimal places in the blank. For example, 1.234 would be a legitimate entry.

Question 13 of 20
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.
Complex numbers should be in the form (a + bi) where "a" and "b" need to have explicitly stated values.
For example: {1+1i} is valid whereas {1+i} is not. {0+9i} is valid whereas {9i} is not.

Suppose a firm that produces light bulbs wants to know whether it can say that its light bulbs typically last more than 1500 hours. Hoping to find support for their claim, the firm collects a random sample of n = 25 light bulbs and records the lifetime (in hours) of each bulb. The information related to the hypothesis test is presented below.

Test of H0: 1500 versus H1: > 1500
Sample mean 1509.5
Sample standard deviation 24.27
Assuming the life length of this type of lightbulb is normally distributed, what is the p-value associated with this test? Place your answer, rounded to 3 decimal places in the blank. For example, .123 would be a legitimate entry.

Question 14 of 20
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

A statistician wishes to test the claim that the standard deviation of the weights of firemen is greater than 25 pounds. To do so, she selected a random sample of 20 firemen and found s = 27.2 pounds.

Assuming that the weights of firemen are normally distributed, to test her research hypothesis the statistician would use a chi-square test. In that case, what is the computed test value?

Place your answer, rounded to 3 decimal places, in the blank. For example, 23.456 would be a legitimate entry.

Question 15 of 20

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

The ABC battery company claims that their batteries last at least 100 hours, on average. Your experience with their batteries has been somewhat different, so you decide to conduct a test to see if the company's claim is true. You believe that the mean life is actually less than the 100 hours the company claims. You decide to collect data on the average battery life (in hours) of a random sample of n = 20 batteries. Some of the information related to the hypothesis test is presented below.

Test of H0: 100 versus H1: 100
Sample mean 98.5
Std error of mean 0.777

Assuming the life length of batteries is normally distributed, if you wish to conduct this test using a .05 level of significance, what is the critical value that you should use? Place your answer, rounded to 3 decimal places in the blank. For example, -1.234 would be a legitimate entry.

Question 16 of 20

Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

A firm that produces light bulbs claims that their lightbulbs last 1500 hours, on average. You wonder if the average might differ from the 1500 hours that the firm claims. To explore this possibility you take a random sample of n = 25 light bulbs purchased from this firm and record the lifetime (in hours) of each bulb. You then conduct an appopriate test of hypothesis. Some of the information related to the hypothesis test is presented below.

Test of H0: = 1500 versus H1: 1500
Sample mean 1509.5
Sample Standard Deviation 24.27

Assuming the life length of this type of lightbulb is normally distributed, what is the p-value associated with this test? Place your answer, rounded to 3 decimal places, in the blank. For example, 0.234 would be a legitimate entry.

Question 17 of 20
Accepted characters: numbers, decimal point markers (period or comma), sign indicators (-), spaces (e.g., as thousands separator, 5 000), "E" or "e" (used in scientific notation). NOTE: For scientific notation, a period MUST be used as the decimal point marker.

The CEO of a software company is committed to expanding the proportion of highly qualified women in the organization's staff of salespersons. He believes that the proportion of women in similar sales positions across the country is less than 45%. Hoping to find support for his belief, he directs you to test

H0: p .45 vs H1: p < .45.

In doing so, you collect a random sample of 50 salespersons employed by his company, which is thought to be representative of sales staffs of competing organizations in the industry. The collected random sample of size 50 showed that only 18 were women.

What is the smallest level of significance at which you could reject the null in favor of the alternative hypothesis? Place your answer, rounded to 4 decimal places, in the blank. For example, 0.1234 would be a legitimate entry.

Question 18 of 20
If a null hypothesis about a population mean is rejected at the 0.025 level of significance, then it must also be rejected at the 0.01 level.

True
False

Question 19 of 20
A one-tailed alternative is one that is supported by evidence in either direction.

True
False

Question 20 of 20
The probability of making a Type I error and the level of significance are the same.

True
False

https://brainmass.com/statistics/conditional-probability-distribution/hypothesis-testing-questions-624675

#### Solution Preview

1C
162/200 = 0.81
z = (0.81 - 0.79) / sqrt(0.79 * 0.21 / 200)
z = 0.69

2A
Since the question says "different from 75", we use equal and not equal.

3A
100% - 5% = 95%
If the 95% confidence interval does not include the hypothesized value of the parameter in a 2-tailed test, then the null hypothesis is rejected.

4C
Since the question says "more effective", we use a one-tailed test.

5A
Small p leads to less chance of rejection of null hypothesis, which indicates more evidence in support of the alternative ...

#### Solution Summary

All questions have been answered, and justification given. An Excel file with supporting computations has been provided.

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