Sampling Distributions – Center and Variability Answers

A farmer determines that, on average, his chickens lay a total of 16 eggs each day. A random sample of 10 days was taken, and the mean number of eggs was determined. Let μ = the true mean number of eggs the chickens lay each day. Which of the following values for the sample mean is the least likely to occur?

Students in a large district’s two high schools are offered a "Second Breakfast” program after their first-period class. The district’s nutrition manager is interested in determining if the program is effective. He takes two independent random samples of days from the previous years, 20 from high school A and 15 from high school B, and calculates the mean amount of money, in dollars spent, for the program. Which of the following statements concerning the variability of the sampling distribution of the sample mean is correct?

A farmer determines that, on average, his chickens lay a total of 16 eggs each day. A random sample of 10 days was taken, and the mean number of eggs was 15.1 eggs. Let μ = the true mean number of eggs the chickens lay each day. Under the assumption that the true mean number of eggs is 16, 100 simulated means for samples of size 10 are shown in the dotplot.Using the dotplot, is there evidence that the chickens are laying fewer than 16 eggs?

A statistics teacher has a large container of beads that she says contains 60% blue beads. A student randomly selects 50 beads. Let p = the true proportion of blue beads in the container. If the true proportion of blue beads is 0.60, which value of is least likely to occur?

The owner of an apple orchard knows that the average weight of Granny Smith apples is 380 grams. A random sample of 40 apples was selected and the mean weight was calculated. Let μ = the true mean weight of the Granny Smith apples in the orchard. Which of the following means is least likely to occur if the true mean weight is 380 grams?

The ages of the 5 officers for a school club are 18, 18, 17, 16, and 15. The median of the ages of the officers is 17.0. The table displays all possible samples of size 2 and the corresponding median for each sample.Using the medians in the table, is the sample median an unbiased estimator?

A statistics teacher has a large container of beads that she says contains 60% blue beads. A student randomly selects 50 beads. Let p = the true proportion of blue beads in the container. Under the assumption that the true proportion is 0.60, the student generated 200 values of .What does the dot above 0.74 represent?

The ages of the 5 officers for a school club are 18, 18, 17, 16, and 15. The mean of the ages of the officers is 16.8. The table displays all possible samples of size 2 and the corresponding mean for each sample.Using the means in the table, is the sample mean an unbiased estimator?

A student decides to spin a dime and determine the proportion of times it lands on heads. The student spins the dime 25 times and records that it lands on heads 17 times. Let p = the true proportion of times the dime would land on heads when spun. If the true proportion is 0.5, which of the following sample proportions is the least likely to occur?

A statistics teacher has a large container of beads that she says contains 60% blue beads. A student randomly selects 50 beads, and 25 of them were blue. Let p = the true proportion of blue beads in the container. Under the assumption that the true proportion is 0.60, the student generated 200 values of .Is there evidence that the true proportion of blue beads in the container is less than 0.60?