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Chapter 9: Q. 67. (page 606)

Battery life A tablet computer manufacturer claims that its batteries last an average of 10.5 hours when playing videos. The quality-control department randomly selects 20 tablets from each day鈥檚 production and tests the fully charged batteries by playing a video repeatedly until the battery dies. The quality control department will discard the batteries from that day鈥檚 production run if they find convincing evidence that the mean battery life is less than 10.5 hours. Here are a dot plot and summary statistics of the data from one day:

a. State appropriate hypotheses for the quality-control department to test. Be sure to define your parameter.

b. Check if the conditions for performing the test in part (a) are met.

Short Answer

Expert verified

Part a)H0:渭=10.5Ha:渭<10.5

Part b) Large sample condition is not satisfied.

Step by step solution

01

Part a) Step 1: Given information

The claim is that means is less than10.5

02

Part b) Step 2: The objective is to explain the state appropriate hypothesis for the quality-control department to test. 

The null hypothesis states that the population value is equal to the claim value: H0:渭=10.5

The null hypothesis or the alternative hypothesis is the claim. The null hypothesis asserts that the population means equals the value specified in the claim. If the claim is the null hypothesis, then the alternative hypothesis statement is the inverse of the null hypothesis.

H1:渭<10.5

localid="1654460033100" 渭is the mean battery lifetime.

03

Part b) Step 1: Given information

Given:

04

Part b) Step 2: The objective is to find the conditions for performing the test in part (a) are met

Random, independent (condition), and Normal/ Large sample are the three conditions.

Random: Satisfied because the tablets were chosen at random.

Independent: Satisfied, because the sample of 20 tablets represents less than 10%of the total tablet population.

Normal/large sample size: Dissatisfied because the sample size of 20 tablets is small and the distribution in the dot plot is skewed.

Because the Normal/Large sample condition is not met, a hypothesis test for the population mean is not appropriate.

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Most popular questions from this chapter

Upscale restaurant You are thinking about opening a restaurant and are searching for a good location. From the research you have done, you know that the mean income of those living near the restaurant must be over \(85,000to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50people living near one potential site. Based on the mean income of this sample, you will perform a test at the

伪=0.05 significance level of H0:渭=\)85,000versus Ha:渭>\(85,000, where 渭 is the true mean income in the population of people who live near the restaurant. The power of the test to detect that 渭=\)86,000is 0.64 Interpret this value.

A95%confidence interval for the proportion of viewers of a certain reality television

show who are over 30 years old is (0.26,0.35). Suppose the show's producers want to est the hypothesis \H0:p=0.25against Ha: Ha:p鈮�0.25. Which of the following is an appropriate conclusion for them to draw at the 伪=0.05

a. Fail to reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old equals 0.25

b. Fail to reject H0there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from0.25.

c. Reject H0; there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from 0.25

. d. Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old is greater than 0.25.

e. Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from0.25.

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

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.

A government report says that the average amount of money spent per U.S. household per week on food is about \(158. A random sample of50 households in a small city is selected, and their weekly spending on food is recorded. The sample data have a mean of \)165 and a standard deviation of \(20. Is there convincing evidence that the mean weekly spending on food in this city differs from the national figure of \)158?
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