MATH 1530 Assignment 6

Please complete the assignment (you may print this, type in the document, or complete neatly on notebook paper), scan (preferably using Microsoft Office Lens or CamScanner) or save your work, and submit a PDF or Word document to the Assignments folder labeled Assignment 6 in Brightspace.

Part 1 Comparing 90%, 95%, and 99% Confidence Intervals

A random sample of 15 healthy women at rest had a mean temperature of 98.25F and a standard deviation of 0.72F. Assume the temperature of healthy women at rest is normally distributed.

Construct 90%, 95%, and 99% confidence intervals for the mean.

Display the confidence intervals graphically (you can use the number line or copy and paste from Statcrunch).

Fill in the blank with gets narrower, gets wider or stays the same.

Answers:

90% Conf. Interval:

95% Conf. Interval:

99% Conf. Interval:

b.)

c.) To become more confident that the confidence interval for the mean actually contains the true population mean, , the confidence interval

______________________________ .

Part 2 Determining Minimum Sample Size

You may use Statcrunch or the formula for calculating the minimum sample size needed to have a particular confidence level and stay within a specified margin of error. Show your work, including what you input in Statcrunch if you use Statcrunch.

Statcrunch directions: Stat Proportion Stats One sample Width/sample size

Formula: n= pqzcE2

**Note - width = 2E and Target proportion = p = previous estimate, or 0.5 if no previous estimate

Short Answer (Write 1-2 complete sentences)

When determining the minimum size of the sample needed to estimate a population parameter, we always round up to the next whole number, even if that might violate the usual rounding rules. Why do we have this requirement?

A medical researcher wishes to determine the percentage of women who take vitamins. He wants to be 99% confident that the estimate is within 2 percentage points of the true population proportion. A recent study determined that 25% of women took vitamins. How many women must be surveyed?

You want to estimate, with 95% confidence, the proportion of Canadians that eat sushi 2-3 times a week. You want to keep this estimate within 7% of the true population proportion.

Determine the minimum sample size if no prior estimate is known.

An older study found that 26% of Canadians eat sushi 2-3 per week. Determine the minimum sample size using this prior estimate.