# Question about Confidence interval and t test

Part 1

Biting an unpopped kernel of popcorn hurts! As an experiment, a self-confessed connoisseur of cheap popcorn carefully counted 773 kernels and put them in a popper. After popping, 66 unpopped kernels were counted.

A. Construct a 90% confidence interval for the proportion of all kernels that would not pop.

1. What was the Point Estimate?

2. What was the Margin of error, E =

3. What was the z-value?

4. Confidence Interval?

(write as 0.089 < µ < 0.125)

B. Interpret the confidence interval

C. Check the normality assumption.

Part 2

sample of 19 pages was taken without replacement from the 1,591-page phone directory Ameritech Pages Plus Yellow Pages. On each page, the mean area devoted to display ads was measured (a display ad is a large block of multicolored illustrations, maps, and text).

Construct a 95% confidence interval. The data are shown below:

0 260 356 350 536 0 268 369 428 536

268 396 469 536 162 338 350 536 536

(in square millimeters)

A. Construct a 95% confidence interval for the true mean.

1. What was the Point Estimate?

2. What was the Margin of error, E =

3. What was the t-value?

4. Confidence Interval?

(write as 23 < µ < 45)

B. Interpret the confidence interval

C. What sample size, n, would be needed to obtain an error of ±10 square millimeters with 99% confidence?

(Use Sample Size for a Mean, Doane, Ch. 8, p. 326 and s in place of σ)

1. Sample size, n = [(z)(s)/E]^2

2. What is the sample size, n, using the finite formula?

(N = 1,591 pages)

Sample size, n =

Part 3

Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10 or below.

The firm examined 45 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation, s = 4.45 pages. Is the true mean greater than 10 at a 99% confidence level?

A. Choose the Hypothesis

B. Specify the Decision Rule

C. Calculate the Test Statistic

D. Make the Decision

E. Give an interpretation of the Decision

F. P-value Method

1. Calculate the P-value. What is it?

(There are online calculators or MegaStat)

2. Does that P-value support the Decision in Part D? Explain.

HYPOTHESIS TEST ~ PROPORTIONS

Part 4

Read and understand before responding

+ Lecture Notes

A coin was flipped 80 times and came up heads 50 times. Is the coin biased toward heads at a 90% confidence level?

A. Choose the Hypothesis

B. Specify the Decision Rule

C. Calculate the Test Statistic

D. Make the Decision

E. Give an interpretation of the Decision

F. P-value Method

1. Calculate the P-value. What is it?

2. Does that P-value support the Decision in Part D? Explain.

#### Solution Summary

The solution provides step by step method for the calculation of confidence interval and t test. Formula for the calculation and Interpretations of the results are also included.