1. Geoff is the proud owner of a restaurant. Recently he read an article in Food Weekly which stated that the population mean preparation time for food at popular restaurants is equal to 22 minutes. A footnote at the bottom of the article said that the population standard deviation of preparation times was equal to 7 minutes.

Geoff is interested in determining whether his restaurant has the same average preparation time as the popular restaurants described in the magazine article. Geoff timed how long it took to prepare 38 randomly selected meals over a week. The mean preparation time for the sample was calculated as 21 minutes. Geoff would like to use his sample to construct a hypothesis test with H₀: = 22 and H_a: 22.

a)Calculate the P-value that corresponds to the sample and hypotheses. Give your answer as a decimal to 4 decimal places.

P-value =

b)Using the P-value for Geoff's hypothesis test and a level = 0.05, Geoff should ____ the null hypothesis.

Accept ___

Reject___

Not Reject ___

2. The head of Marketing at American Expresso is interested in determining whether the average income of its credit card holders has increased over the past 15 years. When the credit cards were first marketed, the mean income of all card holders was equal to $55,000 per annum. The results of the corresponding hypothesis test that was carried out are shown here.

------------------------------

INCOME TEST

H0: = $55,000 per a

Ha: > $55,000 per a

= 0.05

x = $57,475 per a = $6,000 per an

n = 35

z = 2.44

P-value = 0.0073

Outcome: Reject the Null

--------------------------------

According to the hypothesis test results, it is most reasonable to conclude that:

there is a 99.27% chance that the mean income of American Expresso credit card holders is now _greater than $55,000 per annum

approximately 99.27% of American Expresso credit card holders have an income greater than $55,000 per annum

there is evidence supporting the hypothesis that the mean income of American Expresso credit card holders is now greater than $55,000 per annum

the mean income of American Expresso credit card holders is now greater than $55,000 per annum

3. The maternity ward of the Royal Prince of Hollywood Hospital is doing a study on the average gestation times of the babies born to its patients. A sample of 45 past patients in the ward have been randomly selected and the gestation times of their babies recorded. The sample mean gestation time was calculated as 267 days. The population standard deviation of gestation times of all babies is known to be 16 days. It is assumed that this standard deviation will also apply specifically to the patients of the maternity ward of the Royal Prince of Hollywood Hospital.

Calculate the upper and lower bounds of the 99% confidence interval for the mean gestation time of babies born in the maternity ward of the Royal Prince of Hollywood Hospital. Give your answers in days to 2 decimal places.

a)Upper Bound = ______ days

b)Lower bound= _______ days

4. The Mean Corporation would like to invest in the booming health food industry. It is considering the creation of a health-drink franchise called Goose Juice. The investment department of the Mean Corporation wants to investigate the feasibility of this venture by examining the profits of similar franchises. It believes that the venture will be feasible if an average annual profit of more than $76,000 can be expected from each Goose Juice that is opened. It is known that the annual profits earned by health-drink franchises has a population standard deviation of $7,600.

The Mean Corporation's statisticians would like to construct a hypothesis test for the mean annual profit () earned by health-drink franchises. A random sample of 30 franchises were

chosen and their annual profit for the previous financial year was recorded. The mean annual profit for the sample was calculated as $77,750. The hypotheses that will be used by the statisticians are H₀: = 76,000 and H_a: > 76,000.

a)Calculate the test statistic (z) that corresponds to the sample and hypotheses. Give your answer to 3 decimal places. Z=_______

b)Using the test statistic for the Mean Corporation's hypothesis test and level = 0.05, the Mean Corp should:

____accept o

____reject

____ not reject

the null hypothesis?

c)If the sample size is increased to 80 (but the sample mean remains unchanged), the Mean Corporation should:

____accept

____reject

____ not reject the null hypothesis?

5. Select whether a one-tailed or two-tailed hypothesis test is most appropriate in the following situations:

a)A pharmacist wants to test whether the effect of a placebo is different from zero.

____ one-tailed

____ two-tailed

b)Holdem Motors wants to test whether the mean time to assemble a car is less than 24 hours.

____ one-tailed

____ two-tailed

c)IHI insurance wants to test whether the mean time to process a claim is less than 7 days.

____ one-tailed

____ two-tailed

6. Batteries R Us is a manufacturer of batteries and are testing a new production technique for their most popular battery type. It is known that the mean lifetime of these batteries made using the previous production technique was 69 hours. The standard deviation in battery lifetime is 5.0 hours and it is assumed that this has not changed. They would like to know whether mean battery lifetime has increased with the new production technique. The following sample data of battery lifetimes has been collected from a random sample of 40 batteries made using the new manufacturing technique.

Battery Lifetime (Hours)

71.2,74.5,72.9,66,80.5,69.3,65.3, 68.1,61.3,69,

65.8,65.,268.3,78,85.2,73.9,69.2, 69.6,72.3,71,

70.8,75.,271.4,68,76.4,69.3,67.3, 69.4,67.1,68.3,

67.,763.5,77.9,66.1,75.8,65.3,76.1, 65.8,70,71.1

Conduct a hypothesis test to test whether the new manufacturing process has increased mean battery lifetime.

a)From the following options, select the correct null and alternate hypotheses for this test:

a.H₀: = 69, H_a: 69

b.H₀: = 69, H_a: < 69

c.H₀: = 69, H_a: > 69

d.H₀: > 69, H_a: = 69

The correct null and alternate hypotheses for this test are: ___A , ___B, ____C, ____D ?

b)Calculate the test statistic. Give your answer to 2 decimal places.

z = ______

c)Calculate the p-value for the test. Give your answer to 4 decimal places. P value = _____

d)Therefore, at a significance level of 0.05 the null hypothesis is ____ Rejected or ____Not Rejected

e)At a significance level of 0.05, from the result of the test you can conclude that there is:

a.____ Proof

b.____ Significant evidence

c.____ Not enough evidence

to conclude that the

____ Population mean battery lifetime

____ Sample mean battery lifetime

has

____ increased

____ decreased

____not changed

7. A lab is testing the amount of a certain active chemical compound in a particular drug that has been recently developed. The manufacturer claims that the average amount of the chemical is 115 mg. It is known that the standard deviation in the amount of the chemical is 5 mg.

A random sample of 38 batches of the new drug is tested and found to have a sample mean concentration of 111.6 mg of the active chemical.

a) Calculate the 95% confidence interval for the mean amount of the active chemical in the drug. Give your answers to 2 decimal places.

b) At a significance level = 0.05, the null hypothesis that the population mean amount of the active chemical in the drug is 115 mg is

____reject

____ not rejected

8. You are working for a government department and your boss, Jane, has asked you to calculate some results on weekly household income across the state, including a 95% confidence interval for the mean weekly household income that she needs to include in a report. She also says that she is not sure exactly what a 95% confidence interval means and would like you to add an explanation.

You have been supplied with a sample of weekly income figures for 110 households. The data is presented here:

Weekly Household Income

1896,2837,2243,1458,1644,1441,913, 2399,1580,1556,1724,

1925,1966,1028,1147,2188,1500,969, 1197,1191,1680,1655,

2468,1801,1959,1490,1259,2467,1955, 1806,2296,1287,1202,

1797,1405,1775,1133,1298,1909,1107, 2261,1245,1305,2212,

1591,1706,1644,440,1347,1293,1021, 2262,1865,2017,1518,

1408,409,1511,1151,1891,2735,56, 1511,2554,1187,1183,

1236,850,2104,1397,798,1589,1122, 2556,1205,1598,1092,

1616,1494,2495,2162,2041,1670,1942, 1274,2508,1478,2066,

2558,1785,1770,1853,1488,1349,1353, 1554,1252,1350,834,

1246,752,1834,943,2372,1728,1914, 2128,1132,1887,1654,

Historically, the standard deviation in weekly household income is $487.

Complete the report to your boss. Give your numeric answers to 2 decimal places.

a.Sent: February 20, 2020 11:10 AM To: Jane Johnson

Subject: Weekly household income results

Dear Jane,

Here are the results gathered from the collected data:

Assuming a population standard deviation in weekly household income of $487, the 95% confidence interval for the mean weekly household income is:

a) ______

b)This means that

____ approximately 95% of sample means will be within the interval given above

____on approximately 95% of days in a given period the stock makes a return within the interval given above

____the population mean weekly household income is definitely within the interval given above

____using a process that gives correct results in 95% of cases, the population mean weekly household income is within the

interval given above

9. A climate researcher knows that it has previously been the case that the mean temperature in his city has been 77.9 F. He suspects that this may no longer be the case and that the mean temperature may now have changed, and he suspects that is has risen in recent times. He collects sample data with the aim of conducting a hypothesis test to examine his suspicions. He will use a level of significance of 0.01 for the test.

Select the correct null and alternate hypotheses for this test:

b.H0: > 77.9 F

Ha: = 77.9 F

c.H0: = 77.9 F

Ha: > 77.9 F

d.H0: = 77.9 F

Ha: 77.9 F

e.H0: 77.9 F

Ha: = 77.9 F

10. A statistician would like to construct a hypothesis test of the mean using the P-value approach. Rank the steps that the statistician can follow to carry out this hypothesis test at a level of significance of . Note that there may be more than one correct answer.

STEPRANK (1-6)

Collect Sample Data______

Draw a conclusion______

Calculate the P-value______

Calculate the test Statistics______

Define the distribution of the test statistic______

Define the null and alternative hypotheses ______