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Chapter 9: Q T9.13 (page 616)

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?

Short Answer

Expert verified

There is enough proof to help the claim that the mean weekly spending on food in this city differs from the national figure of $158.

Step by step solution

01

Step 1:Given information

n=50

x¯=165.00

s=20.00

02

Step 2:Explaination

The hypotheses are

H0:μ=$158

H1:μ≠$158

The value of the test statistic

t=x¯-μ0s/n

=165.00-15820.00/50

=2.475

The P-value is the probability of getting the value of the test statistic, or a value more extreme. The P-value is the number (or interval) in the column title of Table B containing the t-value in the row

n-1=50-1=49>40:

0.01=2×0.005<P<2×0.01=0.02

If the P-value is lesser than the significance level, then the null hypothesis is rejected.

P<0.05=5%⇒RejectH0

There is enough proof to help the claim that the mean weekly spending on food in this city differs from the national figure of$158

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Most popular questions from this chapter

Pressing pills A drug manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The hardness of a sample from each batch of tablets produced is measured to control the compression process. The target value for the hardness is μ=11.5The hardness data for a random sample of 20 tablets from one large batch are

Is there convincing evidence at the 5%level that the mean hardness of the tablets in this batch differs from the target value?

Better parking A local high school makes a change that should improve student satisfaction with the parking situation. Before the change, 37% of the school’s students approved of the parking that was provided. After the change, the principal surveys an SRS of students at the school. She would like to perform a test of H0:p=0.37Ha:p>0.37where p is the true proportion of students at school who are satisfied with the parking

situation after the change.

a. The power of the test to detect that p=0.45 based on a random sample of 200 students and a significance level of α=0.05 is 0.75 Interpret this value.

b. Find the probability of a Type I error and the probability of a Type II error for the test in part (a).

c. Describe two ways to increase the power of the test in part (a).

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.

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’s 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’s 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.

Bags of a certain brand of tortilla chips claim to have a net weight of 14ounces. Net weights vary slightly from bag to bag and are Normally distributed with mean μ . A representative of a consumer advocacy group wishes to see if there is convincing evidence that the mean net weight is less than advertised and so intends to test the hypotheses

H0:μ=14Ha:μ<14

A Type I error in this situation would mean concluding that the bags

a. are being underfilled when they aren’t.

b. are being underfilled when they are.

c. are not being underfilled when they are.

d. are not being underfilled when they aren’t.

e. are being overfilled when they are underfilled
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