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Hi I need some help with my economic statistics homework! I am very confused.1. The mean income per person in the United States is $38,500, and the distribution of incomes follows a normal distribution. A random sample of 14 residents of Wilmington, Delaware, had a mean of $45,500 with a standard deviation of $9,400. At the 0.050 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average?

a. State the null hypothesis and the alternate hypothesis.

b. State the decision rule for 0.050 significance level. (Round your answer to 3 decimal places.)

c. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

d. Is there enough evidence to substantiate that residents of Wilmington, Delaware, have more income than the national average at the 0.050 significance level?

2. According to the Census Bureau, 3.36 people reside in the typical American household. A sample of 25 households in Arizona retirement communities showed the mean number of residents per household was 2.71 residents. The standard deviation of this sample was 1.10 residents. At the .10 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.36 persons?

a. State the null hypothesis and the alternate hypothesis. (Round your answer to 2 decimal places.)

b. State the decision rule for .10 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

c. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

d. Is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.36 persons?

3..In order to conduct a hypothesis test of the population mean, a random sample of 12 observations is drawn from a normally distributed population. The resulting mean and the standard deviation are calculated as 14.7 and 2.0, respectively. Use Table 2.

Use the critical value approach to conduct the following tests at α = 0.05.

H0: μ ≤ 14.0 against HA: μ > 14.0

a-1. Calculate the value of the test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Test statistic

a-2. Calculate the critical value. (Round your answer to 3 decimal places.)

Critical value

a-3. What is the conclusion?

•

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

•

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

•

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

•

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

H0: μ = 14.0 against HA: μ ≠ 14.0

b-1. Calculate the value of the test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Test statistic

b-2. Calculate the critical value(s). (Round your answers to 3 decimal places.)

Critical value(s) ±

b-3. What is the conclusion?

•

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

•

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

•

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

•

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

4. What is the probability of making a Type II error if the null hypothesis is actually true?

Multiple choice: 0 0.05 1 α5. In hypothesis testing, what is the level of significance?

• Multiple choice:It is selected before a decision rule can be formulated.

•

A value between 0 and 1.

•

The risk of rejecting the null hypothesis when it is true.

•

A value symbolized by the Greek letter α.

•

All of the answers apply..

6. Given the following hypotheses:

H0: μ ≤ 10

H1: μ > 10

A random sample of 10 observations is selected from a normal population. The sample mean was 19 and the sample standard deviation 3.4. Using the 0.05 significance level:

a. State the decision rule. (Round your answer to 3 decimal places.)

b. Compute the value of the test statistic. (Negative answers should be indicated by a minus sign. Round your answer to 3 decimal places.)

c. What is your decision regarding the null hypothesis?

a. State the null hypothesis and the alternate hypothesis.

b. State the decision rule for 0.050 significance level. (Round your answer to 3 decimal places.)

c. Compute the value of the test statistic. (Round your answer to 2 decimal places.)

d. Is there enough evidence to substantiate that residents of Wilmington, Delaware, have more income than the national average at the 0.050 significance level?

2. According to the Census Bureau, 3.36 people reside in the typical American household. A sample of 25 households in Arizona retirement communities showed the mean number of residents per household was 2.71 residents. The standard deviation of this sample was 1.10 residents. At the .10 significance level, is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.36 persons?

a. State the null hypothesis and the alternate hypothesis. (Round your answer to 2 decimal places.)

b. State the decision rule for .10 significance level. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

c. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)

d. Is it reasonable to conclude the mean number of residents in the retirement community household is less than 3.36 persons?

3..In order to conduct a hypothesis test of the population mean, a random sample of 12 observations is drawn from a normally distributed population. The resulting mean and the standard deviation are calculated as 14.7 and 2.0, respectively. Use Table 2.

Use the critical value approach to conduct the following tests at α = 0.05.

H0: μ ≤ 14.0 against HA: μ > 14.0

a-1. Calculate the value of the test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Test statistic

a-2. Calculate the critical value. (Round your answer to 3 decimal places.)

Critical value

a-3. What is the conclusion?

•

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

•

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

•

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

•

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

H0: μ = 14.0 against HA: μ ≠ 14.0

b-1. Calculate the value of the test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Test statistic

b-2. Calculate the critical value(s). (Round your answers to 3 decimal places.)

Critical value(s) ±

b-3. What is the conclusion?

•

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

•

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

•

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

•

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

4. What is the probability of making a Type II error if the null hypothesis is actually true?

Multiple choice: 0 0.05 1 α5. In hypothesis testing, what is the level of significance?

• Multiple choice:It is selected before a decision rule can be formulated.

•

A value between 0 and 1.

•

The risk of rejecting the null hypothesis when it is true.

•

A value symbolized by the Greek letter α.

•

All of the answers apply..

6. Given the following hypotheses:

H0: μ ≤ 10

H1: μ > 10

A random sample of 10 observations is selected from a normal population. The sample mean was 19 and the sample standard deviation 3.4. Using the 0.05 significance level:

a. State the decision rule. (Round your answer to 3 decimal places.)

b. Compute the value of the test statistic. (Negative answers should be indicated by a minus sign. Round your answer to 3 decimal places.)

c. What is your decision regarding the null hypothesis?

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