# 8.3-9.3 Confidence Intervals and Hypothesis Testing

# Problem 1

Elaine wants to determine a 99 percent confidence interval for the true proportion *p* of high school students in the area who attend their home basketball games. Out of *n *randomly selected students, she finds that exactly half attend their home basketball games. About how large would *n *have to be to get a margin of error less than 0.01 for *p*?

**Note: Use the values for ***z**⋆* **from a z-table or t-table, and round to the smallest integer that works.**

*n **≈ *

## Correct Answers

16590

# Problem 2

For each situation, state the null and alternative hypotheses: (Type ”mu” for the symbol *µ *, e.g. **mu ***> ***1 **for the mean is greater than 1, **mu ***< ***1 **for the mean is less than 1, **mu not ****= 1 **for the mean is not equal to 1. Please do not include units such as ”mm” or ”$” in your answer.)

(a) The diameter of a spindle in a small motor is supposed to be 6 millimeters (mm) with a standard deviation of 0.15mm. If the spindle is either too small or too large, the motor will not work properly. The manufacturer measures the diameter in a sample of 15 spindles to determine whether the mean diameter has moved away from the required measurement. Suppose the sample has an average diameter of 4.51 mm.

*H*_{0} :

*H*_{a} :

(b) Destiny thinks that prices in Springfield are lower than the rest of the country. They read that the nationwide average price of a certain brand of laundry detergent is $55 with standard deviation $2.17. They take a sample from 3 local Springfield stores and find the average price for this same brand of detergent is $20.81.

*H*_{0} :

*H*_{a} :

## Correct Answers

(a) mu = 6; mu not = 6

(b) mu=55; mu<55

# Problem 3

Consider the following hypothesis test. The null hypothesis is ”The mean body temperature for humans is 98.6 degrees Fahrenheit,” and the alternative hypothesis is ”The mean body temperature for humans differs from 98.6 degrees Fahrenheit.” Answer the following questions.

a. ”The mean body temperature for humans in fact is 98.6 degrees Farenheit, but the result of the sampling leads to the conclusion that the mean body temprature for humans differs from 98.6 degrees Farenheit” is a

- A. Type II error
- B. correct decision
- C. Type I error

b. ”The mean body temperature for humans in fact differs from 98.6 degrees Farenheit, and the result of the sampling leads to that conclusion” is a

- A. Type II error
- B. correct decision
- C. Type I error

c. ”The mean body temperature for humans in fact is 98.6 degrees Farenheit, and the result of the sampling does not lead to the rejection of the fact that the mean body temperature is 98.6 degrees Farenheit” is a

- A. Type II error
- B. correct decision
- C. Type I error

d. ”The mean body temperature for humans in fact differs from 98.6 degrees Farenheit, but the result of the sampling fails to lead to that conclusion” is a

- A. Type II error
- B. correct decision
- C. Type I error

## Correct Answers

- C
- B
- B
- A