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Chapter 10: Q. 45 (page 598)

Use the following information to answer the next five exercises. Two metal alloys are being considered as material for ball bearings. The mean melting point of the two alloys is to be compared. 15 pieces of each metal are being tested. Both populations have normal distributions. The following table is the result. It is believed that Alloy Zeta has a different melting point.

At the 1 % significance level, what is your conclusion?

Short Answer

Expert verified

At a 1%significance level, there will be sufficient evidence to reject the null hypothesis. The evidence suggests that the melting point of alloy Gamma differs from that of alloy Zeta.

Step by step solution

01

Given Information

The table is


Sample Mean Melting TemperaturesF0
Population Standard Deviation
Alloy Gamma80095
Alloy Zeta900105
02

Determine at the 1% significance level, what is your conclusion.

1%Reject the null hypothesis because the a>p-value is 0.01>0.00623.

At a 1%significance level, there will be sufficient evidence to reject the null hypothesis. The evidence suggests that the melting point of alloy γdiffers from that of alloy Zeta.

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Most popular questions from this chapter

Use the following information to answer the next 12 exercises: The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites.

Which distribution (normal or Student's t) would you use for this hypothesis test?

Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota.

At a pre-conceived α = 0.05, what is your:

a. Decision:

b. Reason for the decision:

c. Conclusion (write out in a complete sentence):

Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota.

Sketch a graph of the situation. Mark the hypothesized difference and the sample difference. Shade the area corresponding to the p-value.

Use the following informotion to answer the next 12 exercises: The U.S. Center for Disease Control reports that the mean life expectancy was \(47.6\) years for whites born in 1900 and \(33.0\) years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was \(45.3\) years with a standard deviation of \(12.7\) years. Of the 82 nonwhites, the mean life span was \(34.1\) years with a standard deviation of \(15.6\) years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites.

Which distribution (normal or Student's t) would you use for this hypothesis test?

A study is done to determine if Company A retains its workers longer than Company B. Company A samples 15workers, and their average time with the company is five years with a standard deviation of 1.2.Company B samples 20workers, and their average time with the company is 4.5yearswith a standard deviation of 0.8.The populations are normally distributed.

a. Are the population standard deviations known?

b. Conduct an appropriate hypothesis test. At the 5%significance level, what is your conclusion?
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