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In order to do this two groups of people suffering a first episode are selected. There are 55 people in the firstgroup and this group will be administered the new drug. There are 75 people in the second group and thisgroup will be administered a placebo. After one year, 10% of the first group has a second episode and 9% ofthe second group has a second episode. Conduct a hypothesis test to determine, at the significance level 0.01,whether there is reason to believe that the true percentage of those in the first group who suffer a secondepisode is different from the true percentage of those in the second group who suffer a second episode?Select the [Alternative Hypothesis, Value of the Test Statistic].

a) [p1 = p2 , 0.1928]

b) [p1 ≠ p2 , 0.1928]

c) [p1 ≠ p2 , 0.2928]

d) [p1 < p2 , 0.1928]

e) [p1 > p2 , 0.1928]

f) None of the above

Question 8

It has been observed that some persons who suffer acute heartburn, again suffer acute heartburn within oneyear of the first episode. This is due, in part, to damage from the first episode. The performance of a newdrug designed to prevent a second episode is to be tested for its effectiveness in preventing a second episode.In order to do this two groups of people suffering a first episode are selected. There are 55 people in the firstgroup and this group will be administered the new drug. There are 45 people in the second group and thisgroup will be administered a placebo. After one year, 11% of the first group has a second episode and 9% ofthe second group has a second episode. Conduct a hypothesis test to determine, at the significance level 0.1,whether there is reason to believe that the true percentage of those in the first group who suffer a secondepisode is different from the true percentage of those in the second group who suffer a second episode?Select the [Rejection Region, Decision to Reject (RH0) or Failure to Reject (FRH0)].

a) [z < -1.65, RH0]

b) [z < -1.65 and z > 1.65, FRH0]

c) [z > 1.65, FRH0]

d) [z < -1.65 or z > 1.65, FRH0]

e) [z > -1.65 and z < 1.65, RH0]

f) None of the above

Question 9

A private and a public university are located in the same city. For the private university, 1038 alumni weresurveyed and 647 said that they attended at least one class reunion. For the public university, 808 out of 1311

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sampled alumni claimed they have attended at least one class reunion. Is the difference in the sampleproportions statistically significant? (Use α=0.05)

a) Fail to reject the null hypothesis. There is not enough evidence to conclude that there is a difference inthe proportions.

b) There is not enough information to make a conclusion.

c) Reject the null hypothesis which states there is no difference in the proportion of alumni that attendedat least one class reunion in favor of the alternate which states there is a difference in the proportions.

Question 10

Mars Inc. claims that they produce M&Ms with the following distributions:

Brown 30% Red 20% Yellow 20% Orange 10% Green 10% Blue 10%

A bag of M&Ms was randomly selected from the grocery store shelf, and the color counts were:

Brown 25 Red 22 Yellow 21 Orange 13 Green 16 Blue 15

Using the χ2 goodness of fit test to determine if the proportion of M&Ms is what is claimed, what is the teststatistic?

a) χ2 = 3.132

b) χ2 = 5.932

c) χ2 = 3.732

d) χ2 = 1.960

e) χ2 = 11.863

f) None of the above

Question 11

Mars Inc. claims that they produce M&Ms with the following distributions:

Brown 30% Red 20% Yellow 20% Orange 10% Green 10% Blue 10%

A bag of M&Ms was randomly selected from the grocery store shelf, and the color counts were:

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Brown 21 Red 21 Yellow 19 Orange 12 Green 17 Blue 13

Using the χ2 goodness of fit test (α = 0.10) to determine if the proportion of M&Ms is what is claimed.Select the [p-value, Decision to Reject (RH0) or Failure to Reject (FRH0)].

a) [p-value = 0.876, RH0]

b) [p-value = 0.124, RH0]

c) [p-value = 0.124, FRH0]

d) [p-value = 0.062, RH0]

e) [p-value = 0.876, FRH0]

f) None of the above

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PRINTABLE VERSIONQuiz 14

Question 1

State the type of hypothesis test to be used in the following situation:

The Blue Diamond Company advertises that their nut mix contains (by weight) 40% cashews, 15% Brazilnuts, 20% almonds and only 25% peanuts. The truth-in-advertising investigators took a random sample (ofsize 20 lbs) of the nut mix and found the distribution to be as follows: 6 lbs of Cashews, 3 lbs of Brazil nuts,5 lbs of Almonds and 6 lbs of Peanuts. At the 0.01 level of significance, is the claim made by Blue Diamondtrue?

a) Two Sample T Test for Means

b) One Sample Z Test for Means

c) χ2 Goodness of Fit Test

d) One Sample Z Test for Proportions

e) One Sample T Test for Means

f) Two Sample Z Test for Proportions

g) Matched Pairs T Test

h) χ2 Test for Independence

Question 2

State the type of hypothesis test to be used in the following situation:

The community hospital is studying its distribution of patients. A random sample of 317 patients presently inthe hospital gave the following information:

Type of Patient Old Rate of Occurrences Present Number of Occurrences Maternity Ward 20% 65 Cardiac Ward 32% 100 Burn Ward 10% 29 Children's Ward 15% 48 All Other Wards 23% 75

Test the claim at the 5% significance level that the distribution of patients in these wards has not changed.

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a) χ2 Goodness of Fit Test

b) Two Sample Z Test for Proportions

c) Matched Pairs T Test

d) χ2 Test for Independence

e) One Sample Z Test for Proportions

f) One Sample T Test for Means

g) Two Sample T Test for Means

h) One Sample Z Test for Means

Question 3

State the type of hypothesis test to be used in the following situation:

In a certain city, there are about one million eligible voters. A simple random sample of size 10,000 waschosen to study the relationship between gender and participation in the last election. The results were:

Men Women Voted 2792 3591 Didn't Vote 1486 2131

Is there a difference in the proportion of people who voted vs. those that didn't vote?

a) Two Sample Z Test for Proportions

b) χ2 Goodness of Fit Test

c) Two Sample T Test for Means

d) χ2 Test for Independence

e) Matched Pairs T Test

f) One Sample T Test for Means

g) One Sample Z Test for Proportions

h) One Sample Z Test for Means

Question 4

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In a certain city, there are about one million eligible voters. A simple random sample of size 10,000 waschosen to study the relationship between gender and participation in the last election. The results were:

Men Women Voted 2622 3355 Didn't Vote 1377 2646

If we are testing for a relationship between gender and participation in the last election, what is the teststatistic?

a) z = -11.359

b) χ2 = 93.113

c) χ2 = 50.556

d) χ2 = 139.669

e) z = -22.671

Question 5

In a certain city, there are about one million eligible voters. A simple random sample of size 10,000 waschosen to study the relationship between gender and participation in the last election. The results were:

Men Women Voted 2755 3755 Didn't Vote 1433 2057

If we are testing for a relationship between gender and participation in the last election, what is the p-valueand decision at the 5% significance level? Select the [p-value, Decision to Reject (RH0) or Failure to Reject(FRH0)]

a) [p-value = 0.687, RH0]

b) [p-value = 0.224, RH0]

c) [p-value = 0.224, FRH0]

d) [p-value = 0.112, RH0]

e) [p-value = 0.687, FRH0]

Question 6

The Blue Diamond Company advertises that their nut mix contains (by weight) 40% cashews, 15% Brazilnuts, 20% almonds and only 25% peanuts. The truth-in-advertising investigators took a random sample (of

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size 20 lbs) of the nut mix and found the distribution to be as follows: 6 lbs of Cashews, 5 lbs of Brazil nuts,6 lbs of Almonds and 3 lbs of Peanuts. At the 0.05 level of significance, is the claim made by Blue Diamondtrue?Select the [p-value, Decision to Reject (RH0) or Failure to Reject (FRH0)].

a) [p-value = 0.304, RH0]

b) [p-value = 0.152, RH0]

c) [p-value = 0.057, FRH0]

d) [p-value = 0.057, RH0]

e) [p-value = 0.304, FRH0]

Question 7

Quart cartons of milk should contain at least 32 ounces. A sample of 20 cartons contained the followingamounts in ounces. Does sufficient evidence exist to conclude the mean amount of milk in cartons is lessthan 32 ounces at the 5% significance level?The data is: (28.5, 32.2, 31.1, 32.6, 31.4, 31.6, 32.4, 32.4, 28.8, 28.8, 28.8, 28.2, 32.4, 31.8, 32.5, 27.4, 31.6,28.4, 28.7, 28.6)Select the [p-value, Decision to Reject (RH0) or Failure to Reject (FRH0)].

a) [p-value = 0.001, RH0]

b) [p-value = 0.001, FRH0]

c) [p-value = 0.000, RH0]

d) [p-value = 0.999, RH0]

e) [p-value = 0.999, FRH0]

Question 8

Hippocrates magazine states that 37 percent of all Americans take multiple vitamins regularly. Suppose aresearcher surveyed 750 people to test this claim and found that 256 did regularly take a multiple vitamin. Isthis sufficient evidence to conclude that the actual percentage is different from 37% at the 5% significancelevel?Select the [p-value, Decision to Reject (RH0) or Failure to Reject (FRH0)].

a) [p-value = 0.104, FRH0]

b) [p-value = 0.052, RH0]

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c) [p-value = 0.104, RH0]

d) [p-value = 0.052, FRH0]

e) [p-value = 0.154, FRH0]

Question 9

A national computer retailer believes that the average sales are greater for salespersons with a collegedegree. A random sample of 34 salespersons with a degree had an average weekly sale of $3433 last year,while 32 salespersons without a college degree averaged $3399 in weekly sales. The standard deviationswere $468 and $642 respectively. Is there evidence at the 5% level to support the retailer's belief?Select the [p-value, Decision to Reject (RH0) or Failure to Reject (FRH0)].

a) [p-value = 0.404, RH0]

b) [p-value = 0.015, RH0]

c) [p-value = 0.015, FRH0]

d) [p-value = 0.404, FRH0]

e) [p-value = 0.202, RH0]

Question 10

The community hospital is studying its distribution of patients. A random sample of 313 patients presently inthe hospital gave the following information:

Type of Patient Old Rate of Occurrences Present Number of Occurrences Maternity Ward 20% 71 Cardiac Ward 32% 93 Burn Ward 10% 29 Children's Ward 15% 47 All Other Wards 23% 73

Test the claim at the 5% significance level that the distribution of patients in these wards has not changed.Select the [p-value, Decision to Reject (RH0) or Failure to Reject (FRH0)].

a) [p-value = 0.768, FRH0]

b) [p-value = 0.768, RH0]

c) [p-value = 0.384, RH0]

d) [p-value = 0.177, RH0]

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e) [p-value = 0.177, FRH0]

Question 11

In a experiment on relaxation techniques, subject's brain signals were measured before and after therelaxation exercises with the following results:

Person 1 2 3 4 5 Before 42.8 37.8 41.8 41.1 37.3 After 36.2 38.8 43.8 37.7 38.3

Is there sufficient evidence to suggest that the relaxation exercise slowed the brain waves? Assume thepopulation is normally distributed.Select the [p-value, Decision to Reject (RH0) or Failure to Reject (FRH0)].

a) [p-value = 0.253, RH0]

b) [p-value = 0.505, FRH0]

c) [p-value = 0.505, RH0]

d) [p-value = 0.253, FRH0]

e) [p-value = 0.126, RH0]