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?