Prob Stats Tutorial # 2

10 Questions only

Select the null & alternative hypotheses for the following tests:

1. Test if the mean weight of cereal in a cereal box differs from 18 ounces.

• H0: μ ≥ 18; HA: μ < 18

• H0: μ = 18; HA: μ ≠ 18

• H0: μ ≤ 18; HA: μ > 18

2. Test if the stock price increases on more than 60% of the trading days.

• H0: p ≤ 0.60; HA: p > 0.60

• H0: p = 0.60; HA: p ≠ 0.60

• H0: p ≥ 0.60; HA: p < 0.60

3. Test if Americans get an average of less than seven hours of sleep.

• H0: μ ≤ 7; HA: μ > 7

• H0: μ ≥ 7; HA: μ < 7

• H0: μ = 7; HA: μ ≠ 7

Select the null & alternative hypotheses for the following claims:

4. I am going to get the majority of the votes to win this election.

• H0: μ = 0.50; HA: μ ≠ 0.50

• H0: p ≤ 0.50; HA: p > 0.50

• H0: p ≥ 0.50; HA: p < 0.50

5. I suspect that your 10-inch pizzas are, on average, less than 10 inches in size.

• H0: μ = 10; HA: μ ≠ 10

• H0: p ≥ 10; HA: p < 10

• H0: μ ≥ 10; HA: μ < 10

6. I will have to fine the company since its tablets do not contain an average of 250 mg of

ibuprofen as advertised.

• H0: p ≤ 250; HA: p > 250

• H0: p = 250; HA: p ≠ 250

• H0: μ = 250; HA: μ ≠ 250

7. Lie Detector

A polygraph (lie detector) is an instrument used to determine if the individual is telling

the truth.

These tests are considered to be 95% reliable. In other words, if an individual lies, there

is a 0.95 probability that the test will detect a lie.

Let there also be a 0.005 probability that the test erroneously detects a lie even when

the individual is actually telling the truth.

Consider the null hypothesis, "the individual is telling the truth," to answer the following

questions.

a. What is the probability of Type I error?

b. What is the probability of Type II error?

8. Blood Test

The screening process for detecting a rare disease is not perfect.

Researchers have developed a blood test that is considered fairly reliable.

It gives a positive reaction in 98% of the people who have that disease.

However, it erroneously gives a positive reaction in 3% of the people who do not have

the disease.

Answer the following questions using the null hypothesis as "the individual does not

have the disease."

a. What is the probability of Type I error?

b. What is the probability of Type II error?

9. Illegitimate Children

• It is generally believed that no more than 0.50 of all babies in a town in Texas are

born out of wedlock. A politician claims that the proportion of babies that are born

out of wedlock is increasing. Identify the correct null and alternative hypotheses to

test the politician's claim.

• H0: p = 0.5 ; HA: p ≠ 0.5

• H0: p ≤ 0.50; HA: p > 0.50

• H0: p ≥ 0.50; HA: p < 0.50

10. Steroids in sports

A professional sports organization is going to implement a test for steroids. The test

gives a positive reaction in 94% of the people who have taken the steroid. However, it

erroneously gives a positive reaction in 4% of the people who have not taken the

steroid. What is the probability of a Type I and Type II error using the null hypothesis

"the individual has not taken steroids."

• Type I: 4%, Type II: 6%

• Type I: 6%, Type II: 4%

• Type I: 94%, Type II: 4%

• Type I: 4%, Type II: 94%

Thank you