Question

Suppose al's aviation claims their airplanes can hold an average of 602 luggage bags at once. a random sample of 20 airplanes is taken, which leads to a sample mean of 569 bags with a sample standard deviation of 72 bags. using this sample, a test is constructed about whether the actual average number of bags the airplanes can hold is less than what al's aviation claims, using a significance level of 0.01.

What are the null and alternative hypotheses?

Answer 1

The null hypothesis (H0) for Al's Aviation is that the true average number of bags the airplanes can hold is at least 602, and the alternative hypothesis (Ha) is that the true average is less than 602. This sets the stage for a one-tailed hypothesis test at a significance level of 0.01.

Step-by-step explanation:

In the scenario provided, a statistical hypothesis test is being conducted to determine if Al's Aviation's airplanes can hold fewer luggage bags than the company claims. Here, the null hypothesis (H0) is that the true average number of bags the airplanes can hold is equal to or greater than the claimed amount, so H0: μ ≥ 602, where μ denotes the population mean.

The alternative hypothesis (Ha) is that the actual average number of bags is less than what Al's Aviation claims, stated as Ha: μ < 602. These hypotheses are set up for a one-tailed test because the interest is solely in whether the actual value is less than the claimed value.

To conduct the hypothesis test, the sample mean, sample standard deviation, and sample size are taken into account to calculate a test statistic, which is then compared to a critical value or used to calculate a p-value at the 0.01 significance level (α = 0.01). If the p-value is less than α or the test statistic is beyond the critical value in the direction of the alternative hypothesis, the null hypothesis would be rejected in favor of the alternative hypothesis.