The mean weight of all 20-year-old women is 128 pounds. A random sample of 28 vegetarian women who are 20 years old showed a sample mean of 122 pounds with a standard deviation of 15 pounds. Assume the weights are normally distributed.

Conduct a hypothesis test to determine whether the mean weight of vegetarian women is significantly less than the mean weight of all 20-year-old women. Use a 0.05 level of significance.

Follow the steps given in class to conduct a hypothesis test.

The question asks to perform a hypothesis test to see if the mean weight of vegetarian women is significantly less than the mean weight for all 20-year-old women, using a 0.05 level of significance and assuming normal distribution of weights.

Explanation:

The subject of the question involves conducting a hypothesis test in statistics to determine if the mean weight of vegetarian women is significantly less than the average weight of all 20-year-old women. The question provides a sample mean, a sample standard deviation, and the sample size, and asks to perform the test using a 0.05 level of significance.

Assuming a normal distribution, we use a t-test to assess the null hypothesis that the mean weight of the vegetarian women is equal to 128 pounds. The alternate hypothesis is that their mean weight is less than 128 pounds. The steps involve calculating the test statistic, finding the p-value, and comparing it to the significance level to make a decision on the null hypothesis.