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Chapter 9: Q. 115 (page 555)

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 α=0.05 level, is the class’ mean family size greater than the national average? Does the Almanac result remain valid? Why?

Short Answer

Expert verified

There is sufficient evidence to conclude that the mean family size in the U.S is not 3.18.

Step by step solution

01

Given information 

The sample of 24families

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

02

Explanation

State the hypothesis:

The null hypothesis states that the mean family size in the U.S is 3.18. In symbols:

H0:μ=3.18

The alternative hypothesis states that the mean family size in the U.S is not 3.18. In symbols:

H0μ≠3.18

localid="1650279234332" p-value=0.0357

The null hypothesis is rejected as the p-value<0.05

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Most popular questions from this chapter

"Red tide" is a bloom of poison-producing algae-a few different species of a class of plankton called dinoflagellates. When the weather and water conditions cause these blooms, shellfish such as clams living in the area develop dangerous levels of a paralysis-inducing toxin. In Massachusetts, the Division of Marine Fisheries (DMF) monitors levels of the toxin in shellfish by regular sampling of shellfish along the coastline. If the mean level of toxin in clams exceeds 800μg(micrograms) of toxin per kg of clam meat in any area, clam harvesting is banned there until the bloom is over and levels of toxin in clams subside. Describe both a TypeI and a Type IIerror in this context, and state which error has the greater consequence.

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

A recent survey in the N.Y. Times Almanac indicated that 48.8% of families own stock. A broker wanted to determine if this survey could be valid. He surveyed a random sample of 250 families and found that 142 owned some type of stock. At the 0.05 significance level, can the survey be considered to be accurate?

H0:p=0.5,Ha:p≠0.5

Assume the p-value is 0.2564. What type of test is this? Draw the picture of the p-value.

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
See all solutions

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