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1. Assume you need to build...

1. Assume you need to build a confidence interval for a population mean within some given situation. Naturally, you must determine whether you should use either the t-distribution or the z-distribution or possibly even neither based upon the information known/collected in the situation. Thus, based upon the information provided for each situation below, determine which (t-, z- or neither) distribution is appropriate. Then if you can use either a t- or z- distribution, give the associated critical value (critical t- or z- score) from that distribution to reach the given confidence level.

a. 95% confidence n=40 σ unknown population data believed to be normally distributed

Appropriate distribution:

Associated critical value:

b. 99% confidence n=12 σ unknown population data believed to be normally distributed

Appropriate distribution:

Associated critical value:

c. 90% confidence n=150 σ known population data believed to be very skewed

Appropriate distribution:

Associated critical value:

d. 95% confidence n=10 σ unknown population data believed to be skewed right

Appropriate distribution:

Associated critical value:

2. A student researcher is interested in determining the average (µ) GPA of all FHSU students, in order to investigate grade inflation at regional universities. The data below represent the GPA's of thirty randomly selected FHSU students.

2.75 2.65 3.95 1.74 2.66 3.10 2.41 1.57 2.12

4.00 2.21 1.95 3.75 1.45 3.01 2.89 2.66 3.95

2.32 3.44 2.07 0.62 2.72 3.55 3.92 3.41 2.14

a. How do you know that you will need to construct the confidence interval using a t-distribution approach as opposed to a z-distribution?

We want to construct the mean value confidence interval for the GPA's with a 90% confidence level.

b. Determine the best point estimate (average) for the mean GPA.

c. Determine the critical t-value(s) associated with the 90% confidence level.

d. Determine the margin of error.

e. Determine the confidence interval.

f. In a sentence, interpret the contextual meaning of your result to part e above...that is relate the values to this situation regarding the mean GPA's of all FHSU students.

3. Determine the two chi-squared (χ2) critical values for the following confidence levels and sample sizes.

a. 95% and n=60

b. 90% and n=18

4. We are also interested in estimating the population standard deviation (σ) for all FHSU student GPA's. We will assume that GPA's are at least approximately normally distributed. Below are the GPA's.

2.75 2.65 3.95 1.74 2.66 3.10 2.41 1.57 2.12

4.00 2.21 1.95 3.75 1.45 3.01 2.89 2.66 3.95

2.32 3.44 2.07 0.62 2.72 3.55 3.92 3.41 2.14

Out to the right, construct a 90% confidence interval estimate of sigma (σ), the population standard deviation.

5. (Multiple Choice) A hypothesis test is used to test a claim. On a right-tailed hypothesis test with a 1.39 critical value, the collected sample's test statistic is calculated to be 1.89. Which of the following is the correct decision statement for the test?

A. Fail to reject the null hypothesis

B. Claim the alternative hypothesis is true

C. Reject the null hypothesis

D. Claim the null hypothesis is false

6. (Multiple Choice) A hypothesis test is used to test a claim. A P-value of 0.23 is calculated on the hypothesis test with a significance level set at 0.05. Which of the following is the correct decision statement for the test?

A. Fail to reject the null hypothesis

B. Claim the alternative hypothesis is false

C. Reject the null hypothesis

D. Claim the null hypothesis is true

7. (Multiple Choice) Which of the following is not a requirement for using the t-distribution for a hypothesis test concerning μ.

A. Sample is a simple random sample

B. Sample size must be larger than 30

C. The population standard deviation is unknown

a. 95% confidence n=40 σ unknown population data believed to be normally distributed

Appropriate distribution:

Associated critical value:

b. 99% confidence n=12 σ unknown population data believed to be normally distributed

Appropriate distribution:

Associated critical value:

c. 90% confidence n=150 σ known population data believed to be very skewed

Appropriate distribution:

Associated critical value:

d. 95% confidence n=10 σ unknown population data believed to be skewed right

Appropriate distribution:

Associated critical value:

2. A student researcher is interested in determining the average (µ) GPA of all FHSU students, in order to investigate grade inflation at regional universities. The data below represent the GPA's of thirty randomly selected FHSU students.

2.75 2.65 3.95 1.74 2.66 3.10 2.41 1.57 2.12

4.00 2.21 1.95 3.75 1.45 3.01 2.89 2.66 3.95

2.32 3.44 2.07 0.62 2.72 3.55 3.92 3.41 2.14

a. How do you know that you will need to construct the confidence interval using a t-distribution approach as opposed to a z-distribution?

We want to construct the mean value confidence interval for the GPA's with a 90% confidence level.

b. Determine the best point estimate (average) for the mean GPA.

c. Determine the critical t-value(s) associated with the 90% confidence level.

d. Determine the margin of error.

e. Determine the confidence interval.

f. In a sentence, interpret the contextual meaning of your result to part e above...that is relate the values to this situation regarding the mean GPA's of all FHSU students.

3. Determine the two chi-squared (χ2) critical values for the following confidence levels and sample sizes.

a. 95% and n=60

b. 90% and n=18

4. We are also interested in estimating the population standard deviation (σ) for all FHSU student GPA's. We will assume that GPA's are at least approximately normally distributed. Below are the GPA's.

2.75 2.65 3.95 1.74 2.66 3.10 2.41 1.57 2.12

4.00 2.21 1.95 3.75 1.45 3.01 2.89 2.66 3.95

2.32 3.44 2.07 0.62 2.72 3.55 3.92 3.41 2.14

Out to the right, construct a 90% confidence interval estimate of sigma (σ), the population standard deviation.

5. (Multiple Choice) A hypothesis test is used to test a claim. On a right-tailed hypothesis test with a 1.39 critical value, the collected sample's test statistic is calculated to be 1.89. Which of the following is the correct decision statement for the test?

A. Fail to reject the null hypothesis

B. Claim the alternative hypothesis is true

C. Reject the null hypothesis

D. Claim the null hypothesis is false

6. (Multiple Choice) A hypothesis test is used to test a claim. A P-value of 0.23 is calculated on the hypothesis test with a significance level set at 0.05. Which of the following is the correct decision statement for the test?

A. Fail to reject the null hypothesis

B. Claim the alternative hypothesis is false

C. Reject the null hypothesis

D. Claim the null hypothesis is true

7. (Multiple Choice) Which of the following is not a requirement for using the t-distribution for a hypothesis test concerning μ.

A. Sample is a simple random sample

B. Sample size must be larger than 30

C. The population standard deviation is unknown

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