Question

In a representative sample of 50 American households, 32 households had a pet. Use this sample data to answer the following questions.

A. Use Minitab Express to construct a 95% confidence interval to estimate the proportion of all American households with a pet. Show how you checked assumptions. If assumptions were met, use the normal approximation method. Remember to include all relevant Minitab Express output and to clearly identify your answer. Other than checking assumptions, do not do any hand calculations. [15 points]

B. What sample size would be needed to construct a 95% confidence interval to estimate the proportion of all households with a pet with a margin of error of ±1%? Use the observed sample proportion as an estimate for the population proportion. You will need to do hand calculations. Show all of your work. [10 points]

C. A researcher would like to know if there is evidence that more than half of all American households have a pet. Use the five-step hypothesis testing procedure outlined below to address this research question. The only hand calculation you will need to do will be in step 1 to check assumptions. Use Minitab Express for steps 2 and 3. Remember to include all relevant Minitab Express output and to clearly identify your test statistic and p value. [25 points]

Step 1: Check assumptions and write hypotheses

Step 2: Calculate the test statistic

Step 3: Determine the p value

Step 4: Decide to reject or fail to reject the null

Step 5: State a “real world” conclusion

Answer 1

(a) The Minitab output is:

The 95% confidence interval to estimate the proportion of all American households with a pet is between 0.49 and 0.77.

(b) p = 32/50 = 0.64

n = (z/E)^2*p*(1 - p)

n = (1.96/0.01)^2*0.64*(1 - 0.64)

n = 8851

(c) The Minitab output is:

The p-value is 0.032.

Since the p-value (0.032) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that more than half of all American households have a pet.