Sampling Distribution of the Sample Mean — Unit test Answers

The prices of pants at a large clothing store chain are skewed left with a mean of $32 and a standard deviation of $20. The manager at one of the stores randomly selects 30 pairs of pants. What is the shape of the distribution of the sample mean for all possible random samples of size 30 from this population?

The times to pop a regular bag of microwave popcorn without burning it are Normally distributed with a mean time of 140 seconds and a standard deviation of 20 seconds. The times to pop a mini bag of microwave popcorn, without burning it, are Normally distributed with a mean time of 90 seconds and a standard deviation of 15 seconds. Suppose two independent random samples, 25 of each, are taken and the mean popping times are calculated. Let R = the popping time of a randomly selected regular-sized bag and M = the popping time of a mini-sized bag. Which of the following best describes the mean of the sampling distribution of ?

In a large high school, 37% of the teachers believe that five minutes is not enough time for students to change classes. However, 89% of the students believe that five minutes is not enough time for students to change classes. Let and be the sample proportions of teachers and students, respectively, who believe that five minutes is not enough time for students to change classes. Suppose 28 teachers and 100 students are selected at random and asked their opinion on the amount of time students have to change class.Which of the following is the correct shape and justification of the sampling distribution of ?

The weights of bunches of bananas in the grocery store are Normally distributed with a mean weight of 3.54 pounds and a standard deviation of 0.64 pounds. A random sample of four bunches is taken and the mean weight is recorded. Which of the following is the standard deviation of the sampling distribution for the mean of all possible samples of size four?

At a university, 34% of undergraduate students love spicy food, while 45% of graduate students love spicy food. Let and be the sample proportions of undergraduate and graduate students at this university, respectively, who love spicy food. Suppose 35 undergraduate students and 28 graduate students from this university are selected at random and asked if they love spicy food.Which of the following is the correct calculation and interpretation of the standard deviation of the sampling distribution of ?

In a large high school, 37% of the teachers believe that five minutes is not enough time for students to change classes. However, 89% of the students believe that five minutes is not enough time for students to change classes. Let and be the sample proportions of teachers and students, respectively, who believe that five minutes is not enough time for students to change classes. Suppose 28 teachers and 100 students are selected at random and asked their opinion on the amount of time students have to change class.Which of the following is the mean of the sampling distribution of ?

The ages of the 5 officers for a school club are 18, 18, 17, 16, and 15. The minimum of the ages of the officers is 15. The table displays all possible samples of size 2 and the corresponding minimum for each sample.Using the minimums in the table, is the sample minimum an unbiased estimator?

The proportion of students at a large high school who live within five miles of the school is p = 0.19. The principal takes a random sample of 17 students from this school. Which is the best description of the shape for the sampling distribution of ?

The prices of houses in the US is strongly skewed to the right with a mean of $383,500 and a standard deviation of $289,321. A real estate agent takes a random sample of 30 houses and records the mean price. What is the best description for the sampling distribution?

A bottled water company bottles varying sizes of water, from 8-ounce to 1-gallon containers. The company has determined that the mean quantity in their 20-ounce bottles is 20.8 ounces with a standard deviation of 0.6 ounces. The bottling plant manager believes his machines are overfilling the bottles. A random sample of 30 bottles is taken, and the mean number of ounces of water is recorded. Which of the following values of the mean of the sample is most likely to occur if the true mean number of ounces is 20.8?

A bottled water company bottles varying sizes of water, from 8-ounce to 1-gallon containers. The company has determined that the mean quantity in their 20-ounce bottles is 20.8 ounces with a standard deviation of 0.6 ounces. The bottling plant manager believes his machines are overfilling the bottles. A random sample of 30 bottles is taken, and the mean number of ounces of water is determined to be 21. Under the assumption that the true mean ounces of water is 20.8, 100 simulated means for samples of size 30 are shown in the dotplotWhat does the dot above 21 represent?

The manager of a large grocery store wants to inspect an incoming shipment of oranges to determine the proportion of blemishes. One inspector, Mary, takes a random sample of 25 oranges, and another inspector, Pat, takes a random sample of 50 oranges. Which of the following statements about variability of the sample proportion is correct?