I need help with the problems attached for QNT 351. I’ve attached a word document with 6 questions.

1. At the time she was hired as a server at the Grumney Family Restaurant,

Beth Brigden was told, ?You can average $83 a day in tips.? Assume the

population of daily tips is normally distributed with a standard deviation of

$4.07. Over the first 45 days she was employed at the restaurant, the mean

daily amount of her tips was $84.86. At the 0.05 significance level, can Ms.

Brigden conclude that her daily tips average more than $83?

a. State the null hypothesis and the alternate hypothesis.

H0: ? ? 83 ; H1: ? < 83

H0: ? ? 83 ; H1: ? > 83

H0: ? = 83 ; H1: ? ? 83

H0: ? >83 ; H1: ? = 83

b. State the decision rule.

Reject H0 if z < 1.65

Reject H1 if z > 1.65

Reject H1 if z < 1.65

Reject H0 if z > 1.65

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

places.)

Value of the test

statistic d. What is your decision regarding H0?

Do not reject H0

Reject H0

e.

What is the p-value? (Round your answer to 4 decimal places.)

p-value 2. The Rocky Mountain district sales manager of Rath Publishing Inc., a college textbook publishing

company, claims that the sales representatives make an average of 41 sales calls per week on

professors. Several reps say that this estimate is too low. To investigate, a random sample of 38

sales representatives reveals that the mean number of calls made last week was 42. The standard deviation of the sample is 3.9 calls. Using the 0.025 significance level, can we conclude

that the mean number of calls per salesperson per week is more than 41?

H0 : ? ? 41

H1 : ? > 41

1. Compute the value of the test statistic. (Round your answer to 3 decimal

places.)

Value of the test

statistic

2. What is your decision regarding H0?

H0. The mean number of calls is

(Click to select) (Click to select) than 41 per week. 3. A United Nations report shows the mean family income for Mexican

migrants to the United States is $26,700 per year. A FLOC (Farm Labor

Organizing Committee) evaluation of 21 Mexican family units reveals a

mean to be $28,450 with a sample standard deviation of $10,850. Does this

information disagree with the United Nations report? Apply the 0.01

significance level.

a. State the null hypothesis and the alternate hypothesis. H0: ? =

H1: ? ? b. State the decision rule for .01 significance level. (Negative amounts should be

indicated by a minus sign. Round your answers to 3 decimal places.)

Reject H0 if t is not between c. and Compute the value of the test statistic. (Round your answer to 2 decimal

places.)

Value of the test

statistic d. Does this information disagree with the United Nations report? Apply the 0.01

significance level. . This

(Click to select) data the report.

(Click to select) 4. The following information is available.

H0 : ? ? 220

H1 : ? < 220

A sample of 64 observations is selected from a normal population. The sample

mean is 215, and the population standard deviation is 15. Conduct the following test

of hypothesis using the .025 significance level.

a. Is this a one- or two-tailed test?

Two-tailed test

One-tailed test

b. What is the decision rule? (Negative amount should be indicated by a minus

sign. Round your answer to 2 decimal places.)

H0 when z <

(Click to select) c. What is the value of the test statistic? (Negative amount should be indicated

by a minus sign. Round your answer to 3 decimal places.)

Value of the test statistic

d. What is your decision regarding H0?

Do not reject

Reject

e. What is the p-value? (Round your answer to 4 decimal places.)

p-value 5. Given the following hypotheses: H0 : ? ? 10

H1 : ? > 10

A random sample of 10 observations is selected from a normal population. The

sample mean was 12 and the sample standard deviation 3. Using the .05

significance level:

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

Reject H0 if t >

b. Compute the value of the test statistic. (Round your answer to 3 decimal

places.)

Value of the test statistic

c. What is your decision regarding the null hypothesis?

H0. There is

(Click to select) evidence to

(Click to select) conclude that the population mean is greater than 10. 6. Given the following hypotheses:

H0 : ? = 400

H1 : ? ? 400

A random sample of 12 observations is selected from a normal population. The

sample mean was 407 and the sample standard deviation 6. Using the .01

significance level:

a. State the decision rule. (Negative amount should be indicated by a minus

sign. Round your answers to 3 decimal places.)

Reject H0 when the test statistic is the interval (

(Click to select) b. Compute the value of the test statistic. (Round your answer to 3 decimal

places.)

Value of the test

statistic c. What is your decision regarding the null hypothesis? , ). Do not reject

Reject