10 Testing a Single Population Mean

10.12 Exercises


  1. 1.

    From a study released in 1992, it was claimed that the average water consumed by residences in Wisconsin was 125 gallons per week. A researcher at the Wisconsin Department of Natural Resources (DNR) believes that this average has changed. To test the claim, she took a simple random sample of residences and computed the average gallons of water used per week. The sample is given below:

    120 129 137 90 110
    147 103 95 86 118

    At the 10% level, does the sample provide strong evidence for researcher’s claim?

    1. (a)

      What is the population of interest?

    2. (b)

      State the competing hypotheses.

    3. (c)

      What is the direction of extreme?

    4. (d)

      What test will you use, and why is it reasonable to use?

    5. (e)

      Compute the test statistic and corresponding p-value.

    6. (f)

      Sketch the p-value.

    7. (g)

      State your conclusion, i.e., do you reject H0, or fail to reject H0?

    8. (h)

      State the conclusion in a manner appropriate for a scientific journal.

    9. (i)

      What type of error could have been made?

    10. (j)

      Compute and interpret the effect size if a result the significant.


  2. 2.

    Census Bureau data shows that the mean household income in the area served by a shopping mall is $72,500 per year. A market research firm questions shoppers at the mall to find out whether the mean household income of mall shoppers has changed. The sample is given below (householdincome.xlsx):

    73000 110000 48000 101000 120000 99000 55000 78000
    86000 62000 52000 63000 68000 83000 103000 95000
    58000 95000 79000 53000 56000 79000 149000 64000
    65000 116000 83000 51000 41000 72000 92000 112000

    At the 10% level, does the sample provide strong evidence that the mean household of mall shoppers has changed?

    1. (a)

      What is the population of interest?

    2. (b)

      State the competing hypotheses.

    3. (c)

      What is the direction of extreme?

    4. (d)

      What test will you use, and why is it reasonable to use?

    5. (e)

      Compute the test statistic and corresponding p-value.

    6. (f)

      Sketch the p-value.

    7. (g)

      State your conclusion, i.e., do you reject H0, or fail to reject H0?

    8. (h)

      State the conclusion in a manner appropriate for a scientific journal.

    9. (i)

      What type of error could have been made?

    10. (j)

      Compute and interpret the effect size if a result the significant.


  3. 3.

    A credit card company wondered whether giving frequent flyer miles for every purchase would increase card usage, which has a current mean of $2,500 per year. To test the claim, they gave free miles to a simple random sample of credit card customers. The data is given below (cardusage.xlsx):

    2541 2602 2496 2441 2629
    2680 2540 2402 2724 2380
    2454 2437 2549 2609 2784

    At the 10% level, does the sample provide strong evidence that giving frequent flyer miles will increase the average card usage?

    1. (a)

      What is the population of interest?

    2. (b)

      State the competing hypotheses.

    3. (c)

      What is the direction of extreme?

    4. (d)

      What test will you use, and why is it reasonable to use?

    5. (e)

      Compute the test statistic and corresponding p-value.

    6. (f)

      Sketch the p-value.

    7. (g)

      State your conclusion, i.e., do you reject H0, or fail to reject H0?

    8. (h)

      State the conclusion in a manner appropriate for a scientific journal.

    9. (i)

      What type of error could have been made?

    10. (j)

      Compute and interpret the effect size if a result the significant.


  4. 4.

    The EPA reports that the exhaust emissions for a certain car model has a mean of 1.43 grams of nitrous oxide per mile. The car manufacturer claims their new process reduces the mean level of exhaust emitted for this car model. A simple random sample of the new cars was taken and each had exhaust measured for grams of oxide per mile. The data is given below (in exhaust.xlsx):

    1.36 1.31 1.46 1.36 1.40 1.32 1.34
    1.37 1.53 1.33 1.51 1.51 1.40 1.34
    1.45 1.41 1.58 1.34 1.37 1.37 1.38
    1.60 1.32 1.49 1.39 1.52 1.32 1.35
    1.35 1.54 1.58 1.30 1.33 1.38 1.55
    1.41 1.35 1.43 1.35

    At the 5% level, does the sample provide strong evidence for the manufacturer’s claim?

    1. (a)

      What is the population of interest?

    2. (b)

      State the competing hypotheses.

    3. (c)

      What is the direction of extreme?

    4. (d)

      What test will you use, and why is it reasonable to use?

    5. (e)

      Compute the test statistic and corresponding p-value.

    6. (f)

      Sketch the p-value.

    7. (g)

      State your conclusion, i.e., do you reject H0, or fail to reject H0?

    8. (h)

      State the conclusion in a manner appropriate for a scientific journal.

    9. (i)

      What type of error could have been made?

    10. (j)

      Compute and interpret the effect size if a result the significant.