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

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

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

Histogram

Segmented bar chart

Dotplot

Scatterplot

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

The sample is representative of all MSU students.

The distribution of textbook costs reported is roughlysymmetric.

The students were honest in their responses.

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

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

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

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

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

The variability between individuals in our sample woulddecrease.

The variability between means from many samples woulddecrease.

The confidence interval width would decrease.

The center of the confidence interval would decrease.