Final Answer:
(a) This is a one-tailed test.
(b) Null hypothesis (\(H_0\)): The average number of pets in American households is 1.5.
(c) Alternative hypothesis (\(H_1\)): The average number of pets in American households is less than 1.5.
(d) T-test statistic: The specific value would depend on the gathered data, and the calculation is needed.
(e) P-value: The exact value would depend on the calculated t-test statistic.
(f) Conclusion: Compare the p-value to the significance level. If p < 0.10, reject the null hypothesis; otherwise, fail to reject the null hypothesis.
Step-by-step explanation:
Meng is conducting a one-tailed test because he is specifically interested in whether the average number of pets is lower than the reported 1.5. The null hypothesis ((H_0) assumes that the reported average of 1.5 pets is correct, while the alternative hypothesis (H_1) suggests that the average is less than 1.5.
To perform the t-test, Meng needs to gather and analyze the data from the grocery store survey. The t-test statistic will give him the measure of how far his sample average is from the reported average, accounting for the variability within the sample.
The p-value, resulting from the t-test calculation, represents the probability of obtaining the observed results (or more extreme) if the null hypothesis is true. If the p-value is less than the chosen significance level (here, 0.10), Meng would reject the null hypothesis, suggesting that the average number of pets is indeed lower than 1.5 in American households. On the other hand, if the p-value is greater than 0.10, Meng would fail to reject the null hypothesis, implying that there isn't enough evidence to conclude that the average number of pets is lower than 1.5.