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Chapter 9: Q.101 (page 554)

The mean age of De Anza College students in a previous term was 26.6 years old. An instructor thinks the mean age for online students is older than 26.6. She randomly surveys 56 online students and finds that the sample mean is 29.4 with a standard deviation of 2.1. Conduct a hypothesis test.

Short Answer

Expert verified

CI:(28.8, 30.0)

Step by step solution

01

Find H0 and Ha: We want to test if De Anza College students take less than 26.6 years old mean age for them while conducting online classes, on average.

H0:渭=26.6;Ha:渭>26.6

02

Determine the distribution needed: In words, CLEARLY state what your random variable x represents.Let x = the mean age for online students at De Anza College.

Normal: N26.6,2.156

Test statistic:z=9.98

03

Calculate the p-value using the normal distribution for mean RV

p-value=0.0000

In one to two complete sentences, explain what the p-value means for this problem.

If the null hypothesis is true (the mean age is 26.6), then there is a 0.0000 probability that the sample (estimated) mean age is 29.4 or more.

04

Compare α and the p-value:Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.

alphadecisionreason for decision
0.01Reject the null hypothesis.
p-value<0.01

Conclusion: There is sufficient evidence to conclude that the mean age of online students at De Anza College is greater than 26.6 years.

05

Confidence Interval

CI: (28.8, 30.0)

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Most popular questions from this chapter

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test. At a significance level of a = 0.05, what is the correct conclusion?

a. There is enough evidence to conclude that the mean number of hours is more than 4.75

b. There is enough evidence to conclude that the mean number of hours is more than 4.5

c. There is not enough evidence to conclude that the mean number of hours is more than 4.5

d. There is not enough evidence to conclude that the mean number of hours is more than 4.75

It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get less than seven hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students generated a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 5%, do LTCC Intermediate Algebra students get less than

seven hours of sleep per night, on average?

The TypeIIerror is not to reject that the mean number of hours of sleep LTCC students get per night is at least seven when,

in fact, the mean number of hours

a. is more than seven hours.

b. is at most seven hours.

c. is at least seven hours.

d. is less than seven hours.

Suppose the null hypothesis, H0, is: a patient is not sick. Which type of error has the greater consequence, Type Ior TypeII?

Assume the null hypothesis states that the mean is at most 12. Is this a left-tailed, right-tailed, or two-tailed test?

A bathroom scale claims to be able to identify correctly any weight within a pound. You think that it cannot be that

accurate. What type of test would you use?
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