Exercises 1168 to 1172 are based on the following informatio

Exercises 11.68 to 11.72 are based on the following information. Berdowski et al. (2009) reported on a study they conducted for the European Aviation Safety Agency, in which they surveyed thousands of passengers at airports across Europe. They measured the weight of the individual (including shoes and clothing), as well as the weight of his or her carry-on luggage and checked baggage. As part of the study, they compared weights of these factors for passengers flying in the summer and in the winter, and they reported results separately for men, women and children in various age groups. Some results of this study are given in Exercises 11.68 to 11.72. All weights were reported in kilograms.

11.68.

Summary statistics for the weights of the carry-on luggage for the sample of adult male passengers in winter and the sample of adult male passengers in summer were given in Table 4.6 of the report by Berdowski et al. A comparison of the means for the two seasons is shown in the (somewhat modified) Minitab output below. Use it to answer parts (a) to (d).

Do you think the weights of carry-on luggage for men flying in the winter are approximately normally distributed? Explain. (Hint: Remember the Empirical Rule from Chapter 2.)

Are the conditions met for constructing a confidence interval for the difference in means for independent samples? Explain.

Write a sentence or two interpreting the  confidence interval for the difference provided in the output. Be sure to specify the population(s) to which the interval applies.

Using the interval for the difference provided in the output, draw a picture similar to Figure 11.12 and use it to comment on whether it is plausible that the population means for summer and winter are the same.

Solution

The sampling distribution will be approximately normally distributed when the sample size is greater than or equal to 30. Here both the sample sizes are greater than 30. Thus the distribution follows normal.

The required conditions to construct a confidence interval for the difference in means for independent samples are:

Both the samples are SRS.

The samples are independent.

The sampling distribution is approximately normal.

Homogeneity of variance.

Each of the above conditions is satisfied.

The 95% CI suggests that the interval contains the true means difference with 95% confidence.