Question

[2 pts] Narrow confidence intervals give us more precise estimates of our parameter. What two quantities does the researcher control that affect the width of a confidence interval, and how can the researcher change them to result in narrower confidence intervals?

A random sample of 12 MSU students were surveyed and asked “How much did you spend on textbooks this semester?”

What type of plot should be used to display these data? Select all that apply.

Histogram

Segmented bar chart

Dotplot

Scatterplot

In order to create a theoretical confidence interval from these data, what must be assumed? Select one.

The sample is representative of all MSU students.

The distribution of textbook costs reported is roughly symmetric.

The students were honest in their responses.

With this sample size, we can never use theoretical methods of analysis.

[2 pts] Assume it is valid to use a theoretical confidence interval to analyze these data. The sample mean was $284.90 and the sample standard deviation was $96.10. Use these values and a multiplier of 2.201 to create a 95% confidence interval for the true mean.

[2 pts] Interpret the confidence interval in the context of the problem.

[2 pts] What is meant by having “95% confidence” in the interval?

[2 pts] If we had sampled 50 MSU students instead of 12 and gotten the same sample mean and sample standard deviation, which of the following statements would be true? Select all that apply.

The variability between individuals in our sample would decrease.

The variability between means from many samples would decrease.

The confidence interval width would decrease.

The center of the confidence interval would decrease.

Answer 1

[2 pts] Narrow confidence intervals give us more precise estimates of our parameter. What two quantities does the researcher control that affect the width of a confidence interval, and how can the researcher change them to result in narrower confidence intervals?

A random sample of 12 MSU students were surveyed and asked “How much did you spend on textbooks this semester?”

What type of plot should be used to display these data? Select all that apply.

Answer: Histogram

Segmented bar chart

Answer: Dotplot

Scatterplot

In order to create a theoretical confidence interval from these data, what must be assumed? Select one.

The sample is representative of all MSU students.

Answer: The distribution of textbook costs reported is roughly symmetric.

The students were honest in their responses.

With this sample size, we can never use theoretical methods of analysis.

[2 pts] Assume it is valid to use a theoretical confidence interval to analyze these data. The sample mean was $284.90 and the sample standard deviation was $96.10. Use these values and a multiplier of 2.201 to create a 95% confidence interval for the true mean.

=(223.84, 345.96)

[2 pts] Interpret the confidence interval in the context of the problem.

We are 95% confident that the true mean falls in the interval ($223.84, $345.96).

[2 pts] What is meant by having “95% confidence” in the interval?

If we repeat the sampling procedures and construct confidence intervals 100 times , we are sure that 95% of the such intervals contain true mean.

[2 pts] If we had sampled 50 MSU students instead of 12 and gotten the same sample mean and sample standard deviation, which of the following statements would be true? Select all that apply.

The variability between individuals in our sample would decrease.

Answer: The variability between means from many samples would decrease.

Answer: The confidence interval width would decrease.

The center of the confidence interval would decrease.