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Null and Alternative Hypotheses for Various Problems

(1) In the past, the average age of employees of a large corporation has been 40 years. Recently, the company has been hiring older individuals. In order to determine whether there has been an increase in the average age of all the employees, a sample of 64 employees was selected. The average age in the sample was 45 years with a standard deviation of 16 years. Show all your calculations. Let a = .05.

a. State the null and the alternative hypotheses.
b. Compute the test statistic.
c. Using either the p-value or critical approach, test to determine whether or not the mean age of all employees is significantly more than 40 years.

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(2) Identify the null and alternative hypotheses for the following problems.

a. The manager of a restaurant believes that it takes a customer less than or equal to 25 minutes to eat lunch.
b. Economists have stated that the marginal propensity to consume is at least 90ยข out of every dollar.
c. It has been stated that 75 out of every 100 people who go to the movies on Saturday night buy popcorn.

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(3) Nancy believes that the average running time of movies is equal to 140 minutes. A sample of 4 movies was taken and the following running times were obtained. Assume the population of the running times is normally distributed.

150 150 180 170

a. Compute the sample mean and the standard deviation (4 points).
b. State the null and alternative hypotheses (1 point).
c. Using the critical value approach, test the hypotheses at the 10% level of significance (3 points).

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(4) An automobile manufacturer stated that it will be willing to mass produce electric-powered cars if more than 30% of potential buyers indicate they will purchase the newly designed electric cars. In a sample of 500 potential buyers, 160 indicated that they would buy such a product.

a. State the hypotheses for this problem
b. Compute the standard error of .
c. Compute the test statistic.
d. At 95% confidence, what is your conclusion? Should the manufacturer produce the new electric powered car?

Solution Preview

1.
a. State the null and the alternative hypotheses.
Let u be the mean age of all employees, then Ho: u=40 vs. Ha: u>40

b. Compute the test statistic.
test statistic=(45-40)/[16/sqrt(64)]=2.5

c. Using either the p-value or critical approach, test to determine whether or not the mean age of all employees is significantly more than 40 years.
at 0.05 level and df=45-1=44, the critical value=1.68 from t table. since 1.68<2.5 we reject Ho. We have evidence to say that mean age of all employees is significantly more than 40 years

2.
a. The manager of a restaurant believes that it takes a customer less than ...

Solution Summary

The solution gived detailed steps on solving multiple questions on hypothesis testing with 5-step procedure. All formula and calcuations are shown and explained.

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