Sampling Distributions – Center and Variability Answers

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?

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 390 grams. Let μ = the true mean weight of the Granny Smith apples in the orchard. Under the assumption that the true mean weight of Granny Smith apples is 380 grams, 100 simulated means for samples of size 40 are shown in the dotplot.Using the dotplot, is there evidence that the true mean weight of Granny Smith apples is greater than 380 grams?

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?

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 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. He decides to spin the dime again and spins it 100 times. Which of the following is a correct statement about the variability of the sampling distribution?

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?

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 390 grams. Let μ = the true mean weight of the Granny Smith apples in the orchard. Under the assumption that the true mean weight of Granny Smith apples is 380 grams, 100 simulated means for samples of size 40 are shown in the dotplot.What does the dot above 371 represent?

A student wants to investigate the proportion of students who would support a fundraiser at a large high school. Which of the following sample sizes would have the least variability?

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?