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If you have a chance please answer as many as possible, thank you and I really appreciate your help experts!

Question 16 2 pts

In a hypothesis test, the claim is μ≤28 while the sample of 29 has a mean of 41 and a standard deviation of 5.9. In this hypothesis test, would a z test statistic be used or a t test statistic and why?

t test statistic would be used as the sample size is less than 30

t test statistic would be used as the standard deviation is less than 10

z test statistic would be used as the mean is less than than 30

z test statistic would be used as the sample size is greater than 30

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Question 17 2 pts

A university claims that the mean time professors are in their offices for students is at least 6.5 hours each week. A random sample of eight professors finds that the mean time in their offices is 6.2 hours each week. With a population standard deviation of 0.49 hours, can the university’s claim be supported at α=0.05?

No, since the test statistic is in the rejection region defined by the critical value, the null is rejected. The claim is the null, so is not supported

Yes, since the test statistic is not in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported

Yes, since the test statistic is in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported

No, since the test statistic is not in the rejection region defined by the critical value, the null is rejected. The claim is the null, so is not supported

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Question 18 2 pts

A credit reporting agency claims that the mean credit card debt in a town is greater than $3500. A random sample of the credit card debt of 20 residents in that town has a mean credit card debt of $3619 and a standard deviation of $391. At α=0.10, can the credit agency’s claim be supported?

Yes, since p-value of 0.09 is less than 0.55, reject the null. Claim is alternative, so is supported

No, since p-value of 0.09 is greater than 0.10, fail to reject the null. Claim is alternative, so is not supported

Yes, since p-value of 0.19 is greater than 0.10, fail to reject the null. Claim is null, so is supported

No, since p-value of 0.09 is greater than 0.10, reject the null. Claim is null, so is not supported

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Question 19 2 pts

A car company claims that its cars achieve an average gas mileage of at least 26 miles per gallon. A random sample of eight cars from this company have an average gas mileage of 25.6 miles per gallon and a standard deviation of 1 mile per gallon. At α=0.06, can the company’s claim be supported?

No, since the test statistic of -1.13 is close to the critical value of -1.24, the null is not rejected. The claim is the null, so is supported

Yes, since the test statistic of -1.13 is not in the rejection region defined by the critical value of -1.77, the null is not rejected. The claim is the null, so is supported

Yes, since the test statistic of -1.13 is not in the rejection region defined by the critical value of -1.55, the null is rejected. The claim is the null, so is supported

No, since the test statistic of -1.13 is in the rejection region defined by the critical value of -1.77, the null is rejected. The claim is the null, so is not supported

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Question 20 2 pts

A researcher wants to determine if extra homework problems help 8^th
grade students learn algebra. One 8^th grade class has extra homework problems and another 8^th grade class does not. After 2 weeks, the both classes take an algebra test and the results of the two groups are compared. To be a valid matched pair test, what should the researcher consider in creating the two groups?

That the group without extra homework problems receives different instruction

That the group with the extra homework problems has fewer after school activities

That each class has similar average IQs or abilities in mathematics

That each class of students has similar ages at the time of the testing

Answer 1

Q16) In any hypothesis test, if the population standard deviat is unknown and/or if the sample size is < 30, we use the students t test.

Option 1: t test statistic would be used as the sample size is less than 30.

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Q17) Given = 6.5 hours, = 6.2 hours, = 0.49 hours, n = 8, = 0.05

We see the words 'at least'. Based on this the hypothesis is

H0: 6.5   (Claim)

Ha: < 6.5

This is a left tailed test.

The Test Statistic:

Although the population standard deviation is known, the sample size is < 30, hence we use the students t test.

The test statistic is given by the equation:

The Critical Value:   The critical value (Left Tail) at = 0.05, for df = n -1 = 7, tcritical = -1.89

The Decision Rule:   If tobserved is < -1.89, Then Reject H0.

The Decision:   Since tobserved (-1.73) is > -1.89, We Fail to Reject H0.

Option 2: Yes, Since the test statistic is not in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported.

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Q18) Given = $3500, = $3619, s = $391, n = 20, = 0.10

The Hypothesis:

H0: = 3500

Ha: > 3500   (Claim)

This is a right tailed test.

The Test Statistic:

Since the population standard deviation is unknown and the sample size is < 30, hence we use the students t test.

The test statistic is given by the equation:

The p Value: The p value (Right Tail) for t = 1.36, for (df) = n-1 = 19, is; p value = 0.095

The Decision Rule: If P value is < (0.10), Then Reject H0.

The Decision: Since P value is (0.095) < (0.10), We Reject H0.

Option 1: Yes, Since the p value of 0.09 is lesser than 0.10 (the value given is 0.55, kindly check this), reject the null. Claim is alternative, so is supported.

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Q19) Given = 26 miles/gallon, = 25.6 miles/gallon, s = 1 mile/gallon, n = 8, = 0.06

We see the words 'at least'. Based on this the hypothesis is

H0: 26 (Claim)

Ha: < 26

This is a left tailed test.

The Test Statistic:

Since the population standard deviation is known and the sample size is < 30, hence we use the students t test.

The test statistic is given by the equation:

The Critical Value:   The critical value (Left Tail) at = 0.06, for df = n -1 = 7, tcritical = -1.77

The Decision Rule:   If tobserved is < -1.77, Then Reject H0.

The Decision:   Since tobserved (-1.13) is > -1.79, We Fail to Reject H0.

Option 2: Yes, Since the test statistic of -1.13 is not in the rejection region defined by the critical value of -1.77, the null is not rejected. The claim is the null, so is supported.

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Q20) A matched pair t test is one where the same individual is tested under different environments. In this question, 2 different sets of individuals are being tested and hence it cannot be a matched pair t test. Technically what you are asking for should be for a 2 sample t test and in that case Option 4 is the correct answer. That each class of students has similar ages at the time of testing. Kindly check for the correct requirements before answering.

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