similar to others Make into quiz? Content Check Lessons 6.1-6.3

From a large group of people who signed a card saying they intended to quit smoking, a random sample of 1000 people was selected. It turned out that 210 (21%) of the sampled individuals had not smoked over the past 6 months.

Match the corresponding terms:

A pediatrician wants to know the 75th percentile for the distribution of heights of 10-year-old boys, so she selects a sample of 50 10-year-old male patients and calculates that the 75th percentile in the sample is 56 inches.

Match the corresponding terms:

A school newspaper article claims that 60% of the students at a large high school completed their assigned homework last week. Some statistics students want to investigate if this claim is true, so they choose an SRS of 100 students from the school to interview.

When they found that only 45 of the 100 students completed their assigned homework last week, they suspected that the proportion of all students who completed their assigned homework last week is less than the 60% claimed by the newspaper.

To determine if a sample proportion of = 0.45 provides convincing evidence that the true proportion is less than p = 0.60, the class simulated 250 SRSs of size n = 100 from a population in which p = 0.60.

Here are the results of the simulation:

There is one dot on the graph at 0.73. Explain what this dot represents.

Would it be surprising to get a sample proportion of 0.45 or less in an SRS of size 100 when p = 0.60? Explain.

Based on your answer to #4, is there convincing evidence that the proportion of all students who completed their assigned homework last week is less than p = 0.60? Explain.

To investigate if the sample minimum is an unbiased estimator of the population minimum, 1000 SRSs of size n = 10 were selected from the population described. The sample minimum for each of these samples was recorded on the dotplot. The mean of the simulated sampling distribution is indicated by an orange line segment.

Does the sample minimum appear to be an unbiased estimator of the population minimum? Explain your reasoning.

Select both answers.

To investigate if the sample minimum is an unbiased estimator of the population minimum, 1000 SRSs of size n = 10 were selected from the population described. The sample minimum for each of these samples was recorded on the dotplot. The mean of the simulated sampling distribution is indicated by an orange line segment.

What would happen to the sampling distribution of the sample minimum if the sample size were n = 50 instead? Justify with three answers.

(see the dotplot in #7)

What would happen to the sampling distribution of the sample range if the

sample size were n = 5 instead? Justify with three answers.

(see the dotplot in #10)

Would it be appropriate to use a normal distribution to model the sampling distribution

of p-hat, the proportion of orange Skittles in the sample? Justify your answer.

Would it be appropriate to use a normal distribution to model the sampling distribution

of p-hat = the proportion of orders in the last week that were shipped within 3 working days? Justify your answer.

Is the range unbiased? To investigate if the sample range is an unbiased estimator of the population range, 1000 SRSs of size n = 10 were selected from the population described. The sample range for each of these samples was recorded on the dotplot. The mean of the simulated sampling distribution is indicated by an orange line segment.

Does the sample range appear to be an unbiased estimator of the population range?

Explain your reasoning.

Select both answers.

Is the median unbiased? To investigate if the sample median is an unbiased estimator of the population median, 1000 SRSs of size n = 10 were selected from the population described. The sample median for each of these samples was recorded on the dotplot.

The mean of the simulated sampling distribution is indicated by an orange line segment.

Does the sample median appear to be an unbiased estimator of the population median? Explain your reasoning.