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Chapter 9: Q.75 (page 543)

From generation to generation, the mean age when smokers first start to smoke varies. However , the standard deviation pf that age remains constant of around 2.1years . A survey of 40smokers of this generation was done to see if the mean starting age is at least 19. the sample mean was 18.1 with a sample standard deviation of1.3do the data support the claim at the 5%level?

Short Answer

Expert verified

The true mean is significantly less than 19.

Step by step solution

01

Given Information

From the question itself we are given,

X=18.1represents the mean height for the sample .

s=1.3represents the sample standard deviation for the sample.

蟽=2.1represents the population standard deviation for the sample .

n=40represents the sample size .

渭0=68represents the value that we want to test.

伪=0.05represents the significance level for the hypothesis test.

twould represent the statistic ( variable of interest)

pvrepresents the p value for the test

02

Explanation

H0=渭鈮�19H0=渭<19

The statistic is given by:

z=X炉-渭慰蟽nz=18.1-192.140z=-2.71

Since it is a one sided test the p value would be ;

pv=P(z<-2.71)pv=0.0033

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Most popular questions from this chapter

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 surveys56online students and finds that the sample mean is29.4with a standard deviation of 2.1. Conduct a hypothesis test.

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, the TypeIerror is:

a. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher

b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same

c. to conclude that the mean hours per week currently is 4.5, when in fact, it is higher

d. to conclude that the mean hours per week currently is no higher than , when in fact, it is not higher

Assume the null hypothesis states that the mean is at least 18. Is this a left-tailed, right-tailed, or two-tailed test?

According to the N.Y. Times Almanac the mean family size in the U.S. is 3.18. A sample of a college math class resulted in the following family sizes:

5;4;5;4;4;3;6;4;3;3;5;5;6;3;3;2;7;4;5;2;2;2;3;2

At 伪=0.05 level, is the class鈥� mean family size greater than the national average? Does the Almanac result remain valid? Why?

Previously, an organization reported that teenagers spent 4.5hours 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 4.75hours with a sample standard deviation of 2.0. Conduct a hypothesis test, the Type I error is:

a. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher

b. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same

c. to conclude that the mean hours per week currently is 4.5, when in fact, it is higher

d. to conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher
See all solutions

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