1. A decade-old study found that the proportion of high school seniors who felt that "getting rich" was an important personal goal was 69%. Suppose that we have reason to believe that this proportion has changed, and we wish to carry out a hypothesis test to see if our belief can be supported. State the null hypothesis Ho and the alternative hypothesis H1 that we would use for this test.
Ho=
H1=

2. The breaking strengths of cables produced by a certain manufacturer have a mean, micro sign , of 187 pounds, and a standard deviation of 55 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 26 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1883 pounds. Assume that the population is normally distributed. Can we support, at the 0.01 level of significance, the claim that the mean breaking strength has increased? (Assume that the standard deviation has not changed.)
Perform a one-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places

the null hypothesis: Ho=
the alternative hypothesis: H1=
type of test statistic=
the value of the test statistic: round to three demcimals=
the p value;round to three decimals=
can we support the claim that the mean breaking strength has increased?

3. Citrus Rental is a popular car rental agency that has a history of having too few cars available, so that its available cars are overdriven. The mean monthly mileage over the years for Citrus cars has been about 1550 miles per month.
Recently, though, Citrus purchased thousands of new cars, and the company claims that the average mileage of its cars is now less than in the past. To test this, a random sample of 20 recent mileages of Citrus cars was taken. The mean of these 20 mileages was 1445 miles per month, and the standard deviation was 248 miles per month.

Assume that the population of recent monthly mileages of Citrus cars is normally distributed. At the 0.01 level of significance, can it be concluded that the mean recent monthly mileage, micro sign, of Citrus cars is less than 1550 miles per month?

Perform a one-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places

the null hypothesis: Ho=
the alternative hypothesis: H1
type of test statistic=
the value of the test statistic=
the p-value=
at the 0.01 level of significance, can it be concluded that the mean recent monthly mileage of citrus cars is less than 1550 miles per month?

4. A decade-old study found that the proportion, p, of high school seniors who believed that "getting rich" was an important personal goal was 80%. A researcher decides to test whether or not that percentage still stands. He finds that, among the 230 high school seniors in his random sample, 167 believe that "getting rich" is an important goal. Can he conclude, at the 0.05 level of significance, that the proportion has indeed changed?
Perform a two-tailed test. Then fill in the table below.

Carry your intermediate computations to at least three decimal places

the null hypo: Ho=
the alternative hypo: H1=
type of tet statistic=
the two critical values at the 0.05 level of significance
can we conclude that a portion of high school seniors who believe that getting rich is a goal that has changed?

5. A study conducted by the research department of a pharmaceutical company claims that the annual spending (per person) for prescription drugs for allergy relief, mu1, is greater than or equal to the annual spending (per person) for non-prescription allergy relief medicine, mu2. A health insurance company conducted an independent study and collected data from a random sample of 290 individuals for prescription allergy relief medicine. The sample mean is found to be 17.8 dollars/year, with a sample standard deviation of 5.4 dollars/year. They have also collected data for non-prescription allergy relief medicine. An independent random sample of 240 individuals yielded a sample mean of 18.2 dollars/year, and a sample standard deviation of 4 dollars/year. Since the sample size is quite large, it is assumed that the population standard deviation of the sales (per person) for prescription and non-prescription allergy relief medicine can be estimated by using the sample standard deviation values given above. Is there sufficient evidence to reject the claim made by the research department of the company, at the 0.1 level of significance? Perform a one-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places.

the null hypo: Ho=
the alternative hypo: H1=
type of test statistic=
the value of the test statistic=
the p-value=
can we reject the claim that the mean spending on prescription relief medication is greater than or equal to the mean spending on non-precription allergy relief medication

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