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Chapter 9: Q.74 (page 543)

A particular brand of tires claims that its deluxe tire averages at least 50,000miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. From the 28tires surveyed, the mean lifespan was 46,500miles with a standard deviation of 9,800miles. Using alpha =0.05, is the data highly inconsistent with the claim?

Short Answer

Expert verified

No, the data is not highly inconsistent with the claim.

Step by step solution

01

Given Information

Null hypothesis H0: 渭鈮�50000

Alternate Hypothesis (H伪):渭<50000,it is left-tailed test

02

Explanation

Since the p-value (0.0130)<the alpha value(0.05), the H0 value is rejected.

The Confidence Interval (CI) for population mean (渭)is:

sample mean

=46700卤1.96脳80032

=46700卤2772

03

Conclusion

Lower boundary is 46700-2772=43928

Upper boundary is 46700+2772=49472

The CI is (43928,49472)

Since the claimed average of 50000does not fall within boundaries of the confidence interval , the inference that the data does not support the claim of 5%level could be drawn.

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Most popular questions from this chapter

Some of the following statements refer to the null hypothesis, some to the alternate hypothesis. State the null hypothesis, H0, and the alternative hypothesis. Ha, in terms of the appropriate parameter (渭orp).

a. The mean number of years Americans work before retiring is 34.

b. At most 60% of Americans vote in presidential elections.

c. The mean starting salary for San Jose State University graduates is at least \(100,000 per year.

d. Twenty-nine percent of high school seniors get drunk each month.

e. Fewer than 5% of adults ride the bus to work in Los Angeles.

f. The mean number of cars a person owns in her lifetime is not more than ten.

g. About half of Americans prefer to live away from cities, given the choice.

h. Europeans have a mean paid vacation each year of six weeks.

i. The chance of developing breast cancer is under 11% for women.

j. Private universities' mean tuition cost is more than \)20,000 per year.

H0:p=0.5,Ha:p鈮�0.5

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

The Weather Underground reported that the mean amount of summer rainfall for the northeastern US is at least 11.52 inches. Ten cities in the northeast are randomly selected and the mean rainfall amount is calculated to be 7.42 inches with a standard deviation of 1.3 inches. At the 伪=0.05 level, can it be concluded that the mean rainfall was below the reported average? What if 伪=0.01? Assume the amount of summer rainfall follows a normal distribution.

Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin?

After conducting the test, your decision and conclusion are

a. Reject H0: There is sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.

b. Do not reject H0: There is not sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.

c. Do not reject H0: There is not sufficient evidence to conclude that more than 30% of teen girls smoke to stay thin.

d. Reject H0: There is sufficient evidence to conclude that less than 30% of teen girls smoke to stay thin.

A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening night midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 of them attended the midnight showing. At a 1% level of significance, an appropriate conclusion is:

a. There is insufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is less than 20%.

b. There is sufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is more than 20%.

c. There is sufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is less than 20%.

d. There is insufficient evidence to conclude that the percent of EVC students who attended the midnight showing of Harry Potter is at least 20%.
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