# Elements of Statistics–FHSU Virtual College– Assume you need to build a confidence interval for a population mean

Question

Unit 3 Problem Set

NAME:

Elements of Statistics–FHSU Virtual College–Summer 2015

REMEMBER, these are assessed preparatory problems related to the content of Unit 3. The Unit 3 Exam will consist of similar types of problems, but not exactly the same. Thus, make sure you are thinking about the concepts and procedures you studied in this unit versus simply “copying” the process of an example problem. Also, take time to examine the complete objective list in the Unit 3 Review document. Listed out to the left of the spreadsheet are text chapter separators if you find yourself needing some direction to a related resource. All answers should be calculated, as needed, within this Excel sheet, and final concluding answers given directly below or to the right of the problem. Please make your answers are easily found–for example use a different color or type of font. No numerical answer resulting from a calculation will be accepted unless the process is performed in Excel and formulas/calculations used are evident when the cell is selected.

Also, note that the templates for hypothesis testing provided in the Excel Guides for this unit are also given in the next worksheet in this document–see folder tabs at the bottom of the sheet. You may use these templates by copying from the second worksheet, pasting the copy to the right of the associated problem, then changing values as needed.

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

Appropriate distribution:

Associated critical value:

b. 95% confidence n=10 ? unknown population data believed to be skewed right

Appropriate distribution:

Associated critical value:

c. 95% confidence n=40 ? unknown population data believed to be normally distributed

Appropriate distribution:

Associated critical value:

d. 99% confidence n=12 ? unknown population data believed to be normally distributed

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 2.55 3.95 1.74 2.66 3.10 2.41 1.57 2.12

4.00 3.21 1.95 3.75 1.45 3.01 2.29 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 (?2) critical values for the following confidence levels and sample sizes.

a. 90% and n=60

b. 95% and n=18

4. We are also interested in estimating the population standard deviation (?) 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 2.55 3.95 1.74 2.66 3.10 2.41 1.57 2.12

4.00 3.21 1.95 3.75 1.45 3.01 2.29 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 (?), 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 1.15. Which of the following is the correct decision statement for the test?

A. Fail to reject the null hypothesis

B. Reject the null hypothesis

C. Claim the alternative hypothesis is true

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. Claim the null hypothesis is true

B. Claim the alternative hypothesis is false

C. Reject the null hypothesis

D. Fail to reject the null hypothesis

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

A. Sample size must be larger than 30

B. Sample is a simple random sample

C. The population standard deviation is unknown

8. In an effort to promote healthy lifestyles, health screenings are given to employees of a large corporation. In running a promotional trial, 74 out of the 130 people who work in one office for the corporation participate in the health screening.

a. Is the above information sufficient for you to be completely certain that more than 50% of all employees of the corporation will participate in the health screening? Why or why not?

b. In establishing a statistical hypothesis testing of this situation, give the required null and alternative hypotheses for such a test, if it is desired that more than 50% of the employees participate in the health screening.

H0:

H1:

c. Based on your answer in part b, should you use a right-tailed, a left-tailed, or a two-tailed test? Briefly explain how one determines which of the three possibilities is to be used.

d. Describe the possible Type I error for this situation–make sure to state the error in terms of the percent of employees in the corporation who will participate in the health screenings.

e. Describe the possible Type II error for this situation–make sure to state the error in terms of the percent of employees in the corporation who will participate in the health screenings.

f. Determine the appropriate critical value(s) for this situation given a 0.025 significance level.

g. Determine/calculate the value of the sample’s test statistic.

h. Detemine the P-value.

i. Based upon your work above, is there statistically sufficient evidence in this sample to support that more than 50% of employees will participate in the health screening? Briefly explain your reasoning.

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