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Chapter 9: Q 47. (page 582)

Cell-phone passwords A consumer organization suspects that less than half of parents know their child鈥檚 cell-phone password. The Pew Research Center asked a random sample of parents if they knew their child鈥檚 cell-phone password. Of the 1060parents surveyed, 551reported that they knew the password. Explain why it isn鈥檛 necessary to carry out a significance test in this setting.

Short Answer

Expert verified

Sample proportion is larger than0.5

Step by step solution

01

Given Information

It is given that n=1060

x=551

Claim is less than50%

02

Calculation and Explanation

The claim can be either null or alternate hypothesis.

Null Hypothesis: H0:p=50%=0.5

Alternative Hypothesis: H1:p<0.5

Sample proportion is calculated as:

p^=xn=5511060=0.5198

As claim is less than 0.5and sample proportion is greater than 0.5.

So, there is no proof provided by sample proportion that alternative hypothesis can be true.

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Most popular questions from this chapter

Based on the P-value in Exercise 31, which of the following would be the most

appropriate conclusion?

a. Because the P-value is large, we reject H0. We have convincing evidence that more than 50%of city residents support the tax increase.

b. Because the P-value is large, we fail to reject H0. We have convincing evidence that more than 50%of city residents support the tax increase.

c. Because the P-value is large, we reject H0. We have convincing evidence that at most 50%of city residents support the tax increase.

d. Because the P-value is large, we fail to reject H0. We have convincing evidence that at most 50%of city residents support the tax increase.

e. Because the P-value is large, we fail to reject H0. We do not have convincing

evidence that more than 50%of city residents support the tax increase.

Powerful potatoes Refer to Exercise 85. Determine if each of the following

changes would increase or decrease the power of the test. Explain your answers.

a. Change the significance level to 伪=0.10

b. Take a random sample of 250 potatoes instead of 500 potatoes.

c. The true proportion is p=0.10 instead of p=0.11

Walking to school A recent report claimed that 13%of students typically walk to school. DeAnna thinks that the proportion is higher than 0.13at her large elementary school. She surveys a random sample of 100students and finds that 17typically walk to school. DeAnna would like to carry out a test at the 伪=0.05significance level of H0:p=0.13versus Ha:p>0.13, where p= the true proportion of all students at her elementary school who typically walk to school. Check if the conditions for performing the significance test are met.

Don't argue! A Gallup poll report revealed that 72%of teens said they seldom or never argue with their friends. 3Yvonne wonders whether this result holds true in her large high school, so she surveys a random sample of 150students at her school.

state appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest

Which of the following is not a condition for performing a significance test about an unknown population proportion p?

(a) The data should come from a random sample or randomized experiment.

(b) Individual measurements should be independent of one another.

(c) The population distribution should be approximately Normal, unless the sample size is large.

(d) Both np and n(1 - p) should be at least 10.

(e) If you are sampling without replacement from a finite population, then you should sample no more than 10% of the population.
See all solutions

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