# FINANCE

4.

Consider the following hypotheses:

H0: μ = 1,800

HA: μ ≠ 1,800

The population is normally distributed with a population standard deviation of 440. Compute the value of the test statistic and the resulting p-value for each of the following sample results. For each sample, determine if you can “reject/do not reject” the null hypothesis at the 10% significance level. Use Table 1.(Negative values should be indicated by a minus sign. Round intermediate calculations to 4 decimal places. Round “test statistic” values to 2 decimal places and “p-value” to 4 decimal places.)

Test Statistic p-value

a. = 1,850; n = 110

b. = 1,850; n = 280

c. = 1,650; n = 32

d. = 1,700; n = 32

________________________________________rev: 08_21_2013_QC_33738

5.

Consider the following hypotheses:

H0: μ = 120

HA: μ ≠ 120

The population is normally distributed with a population standard deviation of 46. Use Table 1.

a. Use a 5% level of significance to determine the critical value(s) of the test. (Round your answer to 2 decimal places.)

Critical value(s) ±

b-1. Calculate the value of the test statistic with = 132 and n = 50. (Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

Test statistic

b-2. What is the conclusion at α = 0.05?

Reject H0 since the value of the test statistic is greater than the critical value.

Reject H0 since the value of the test statistic is smaller than the critical value.

Do not reject H0 since the value of the test statistic is greater than the critical value.

Do not reject H0 since the value of the test statistic is smaller than the critical value.

c. Use a 10% level of significance to determine the critical value(s) of the test. (Round your answer to 2 decimal places.)

Critical value(s) ±

d-1. Calculate the value of the test statistic with = 108 and n = 50. (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

Test statistic

d-2. What is the conclusion at α = 0.10?

Reject H0 since the value of the test statistic is not less than the negative critical value.

Reject H0 since the value of the test statistic is less than the negative critical value.

Do not reject H0 since the value of the test statistic is not less than the negative critical value.

Do not reject H0 since the value of the test statistic is less than the negative critical value.

6.

A local bottler in Hawaii wishes to ensure that an average of 16 ounces of passion fruit juice is used to fill each bottle. In order to analyze the accuracy of the bottling process, he takes a random sample of 48 bottles. The mean weight of the passion fruit juice in the sample is 15.80 ounces. Assume that the population standard deviation is 0.8 ounce. Use Table 1.

Use the critical value approach to test the bottler’s concern at α = 0.05.

a. Select the null and the alternative hypotheses for the test.

H0: μ ≤ 16; HA: μ > 16

H0: μ ≥ 16; HA: μ < 16

H0: μ = 16; HA: μ ≠ 16

b-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

Test statistic

b-2. Find the critical value(s). (Round your answer to 2 decimal places.)

Critical value(s) ±

b-3. What is the conclusion?

Reject H0 since the value of the test statistic is not less than the negative critical value.

Reject H0 since the value of the test statistic is less than the negative critical value.

Do not reject H0 since the value of the test statistic is not less than the negative critical value.

Do not reject H0 since the value of the test statistic is less than the negative critical value.

c. Make a recommendation to the bottler.

The accuracy of the bottling process is .

7.

Access the hourly wage data on the below Excel Data File (Hourly Wage). An economist wants to test if the average hourly wage is less than $22.

Click here for the Excel Data File

a. Select the null and the alternative hypotheses for the test.

H0: μ ≤ 22; HA: μ > 22

H0: μ = 22; HA: μ ≠ 22

H0: μ ≥ 22; HA: μ < 22

b. Use the Excel function Z.TEST to calculate the p-value. Assume that the population standard deviation is $6. (Round your answer to 4 decimal places.)

p-value

c. At α = 0.05 what is the conclusion?