Question

1. An airline is interested in knowing the average weight of the carry-on baggage for its customers. Historically, the average weight for carry-on baggage was 15.5 pounds (lbs.), but the airline believes that the average has since increased. A sample of 30 customers was gathered, and it was determined that the average weight for the carry-on baggage for these customers was 16.8 lbs. with a standard deviation of 4.1 lbs.

a.If you were to create a confidence interval for the true average weight of carry-on baggage for this airline, which test statistic would you use?

b.If you found that the 95% confidence interval to estimate the true average weight of carry-on baggage at this airline was (15.27, 18.33), does this provide evidence for the airlines claim or not? Explain your answer.

c.State your null and alternative hypotheses for a hypothesis test given the above information.

d.If you found a p-value of 0.045, what would you conclude if your level of significance was 0.05? Do not forget a contextual interpretation.

Answer 1

Solution:

a.If you were to create a confidence interval for the true average weight of carry-on baggage for this airline, which test statistic would you use?

Answer: We would use the t-statistic because the population standard deviation is unknown.

b.If you found that the 95% confidence interval to estimate the true average weight of carry-on baggage at this airline was (15.27, 18.33), does this provide evidence for the airline's claim or not?

Answer: Since the confidence interval contains the value of 15.5, therefore, we fail to reject the null hypothesis and conclude that there is not sufficient evidence for the airline's claim to be true.

c.State your null and alternative hypotheses for a hypothesis test given the above information.

Answer: The null and alternative hypotheses are:

d.If you found a p-value of 0.045, what would you conclude if your level of significance was 0.05?

Answer: Since the p-value is less than the significance level, we, therefore, reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the average has since increased.