# To use Excel to perform a test of hypotheses concerning the means of two populations

Note – This assignment has 25 points available. Your score will be scaled down to a number out of 10 points.

Goal – To use Excel to perform a test of hypotheses concerning the means of two populations. Excel functions

- 2-sample Z-test (Independent samples, 12 and 2known) – From the menu select: Data → Data Analysis → z-Test: Two Sample for Means
- Pooled T-test (Independent samples, 12 and 2unknown but equal) – From the menu select:Data → Data Analysis → t-Test: Two-Sample Assuming Equal Variances
- Paired T-test (Dependent samples) – From the menu select: Data → Data Analysis → t-Test: Paired Two Sample for MeansProblem 1 – The time it takes for general anesthesia to work (time to induction) is an important consideration during an emergency and for scheduled surgeries. Recently, a study was conducted to compare the mean induction time of similar drugs administered via (1) inhalation and (2) intravenously. Independent random samples of patients requiring general anesthesia were obtained, and the induction times (in minutes) were measured. The data is in the file Excel Homework 6 – Problem 1. Assume the variance in induction time for inhalation administration is 12 = 0.0625 and for intravenous administration is 2= 0.1225. Is there any evidence to suggest that the mean time to induction for inhalation administration is more than the mean time to induction for intravenous administration? Use = 0.05.Create the Output [2 points]

- Download the data file from the Blackboard page for the course.
- Make your header – enter your name and information into cells A1 to A5 (just as you did for theprevious Excel homework assignments).
- Use the appropriate Excel function to produce the needed output. Position the output to the rightof the data (e.g. cell D7). Also, widen the columns so all the information can be read and make sure the output will fit on one page.Questions – write your answers to the following directly on your output. Be neat and label your answers.

- (a) Give the null and alternative hypotheses. [1 point]
- (b) Find and circle the test statistic and the p-value for this test. [1 point]
- (c) Give the decision for the test. Write a conclusion that relates your decision to the context of theproblem. [2 points]

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Problem 2 – Low-carbohydrate foods are very popular as many Americans try to avoid this sugar and starch combination that many believe causes weight gain. An advertisement for a low-carb ice cream claims that the product has 16 fewer grams of carbohydrates per serving than the leading store brand. To check this claim, independent random samples of each type of ice cream were obtained, and the amount of carbohydrates in each serving was measured. The data is in the file Excel Homework 6 –Problem 2. The variance in carbohydrates per serving for the (1) store brand is known to be 8.5 and for the (2) low-carb brand it’s known to be 0.253. Is there any evidence to suggest that the difference in population means of carbohydrates per serving is not 16 grams? Use = 0.05.

Create the Output [2 points]

- Download the data file from the Blackboard page for the course.
- Make your header – enter your name and information into cells A1 to A5 (just as you did for theprevious Excel homework assignments).
- Use the appropriate Excel function to produce the needed output. Position the output to the rightof the data (e.g. cell D7). Also, widen the columns so all the information can be read and make sure the output will fit on one page.Questions – write your answers to the following directly on your output. Be neat and label your answers.

- (a) Give the null and alternative hypotheses. [1 point]
- (b) Find and circle the test statistic and the p-value for this test. [1 point]
- (c) Give the decision for the test. Write a conclusion that relates your decision to the context of theproblem. [2 points]

Problem 3 – The tiny quagga mussels have invaded at least 600 bodies of water in the United States and are causing many problems. These mollusks disrupt the natural food chain, clog pipes, cling to machinery, and foul water-delivery systems. A random sample of quagga mussels was obtained from (1) Lake Texoma and (2) Lake Mead, and the size of each (in cm) was carefully measured. The data is in the file Excel Homework 6 – Problem 3. Is there any evidence to suggest that the population mean size of quagga mussels is larger in Lake Texoma than in Lake Mead? Assume the underlying distributions are normal with equal population variances. Use = 0.05.

Create the Output [2 points]

- Download the data file from the Blackboard page for the course.
- Make your header – enter your name and information into cells A1 to A5 (just as you did for theprevious Excel homework assignments).
- Use the appropriate Excel function to produce the needed output. Position the output to the rightof the data (e.g. cell D7). Also, widen the columns so all the information can be read and make sure the output will fit on one page.

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Questions – write your answers to the following directly on your output. Be neat and label your answers.

- (a) Give the null and alternative hypotheses. [1 point]
- (b) In the story it states that the two population variances are assumed to be equal. Find and circlethe estimate of this common variance. [1 point]
- (c) Find and circle the test statistic and the p-value for this test. [1 point]
- (d) Give the decision for the test. Write a conclusion that relates your decision to the context of theproblem. [2 points]

Problem 4 – A new drug designed to reduce fever (and relieve aches and pains) is being tested for efficacy and side effects. Ten patients entering a hospital with a high fever were selected at random. The temperature (in °F) of each patient was measured, the drug was administered, and two hours later the temperature was measured again. The data is in the file Excel Homework 6 – Problem 4. Assume normality. Conduct the appropriate test of hypotheses to determine whether there is any evidence that the new drug reduces the mean patient temperature after two hours. Use = 0.05.

Create the Output [2 points]

- Download the data file from the Blackboard page for the course.
- Use the appropriate Excel function to produce the needed output. Position the output to the rightof the data (e.g. cell D7). Also, widen the columns so all the information can be read and make sure the output will fit on one page.Questions – write your answers to the following directly on your output. Be neat and label your answers.

- (a) Give the null and alternative hypotheses. [1 point]
- (b) Find and circle the test statistic and the p-value for this test. [1 point]
- (c) Give the decision for the test. Write a conclusion that relates your decision to the context of theproblem. [2 points]

Note – When printing, if your Excel spreadsheets look as though the content you typed has had extra spaces inserted, then see the comment on Excel Homework 1.

keep part 1 in a different excel then part 2

**Part 2 new excel spreadsheet **

Goal – To use Excel to compare the means of several populations by performing a one-way, or single- factor, analysis of variance (ANOVA).

Problem 1 – Many cities, towns, and college campuses use a rotary broom to sweep debris and snow from sidewalks. The pressure created by the broom is one measure of how effective the machine will be in removing debris. Random samples of rotary brooms from four manufacturers were obtained, and the pressure of each broom was measured (in psi). The data is in the file Excel Homework 7 – Problem 1. Do the samples give enough evidence to conclude that at least two population mean pressures are different? Use = 0.05.

Create the Output [2 points]

- Download the data file from the Blackboard page for the course.
- From the menu select: Data → Data Analysis → Anova: Single Factoro Complete the necessary information in the dialog box. The “input range” should includethe column names. Position the output beneath the data (e.g. A16).
- Before printing make sure the output will fit on one page. From the menu select: View → Page Break Preview and drag the dashed page break so as to fit all the output onto one page.
- Note – When printing, if your Excel spreadsheets look as though the content you typed has had extra spaces inserted, then see the comment on Excel Homework 1.Questions – write your answers to the following directly on your output. Be neat and label your answers.

- (a) Give the null and alternative hypotheses. [2 points]
- (b) Find and circle the test statistic and the p-value for this test. [1 point]
- (c) Give the rejection region for the test. (Be sure to describe a region; simply giving a number isnot enough.) [1 point]
- (d) Give the decision for the test. Write a conclusion that relates your decision to the context of theproblem. [2 points]
- (e) Which manufacturer would you recommend? Why? [2 points]