Identify the most appropriate test to use for the ...

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Identify the most appropriate test to use for the following situation: In a experiment on relaxation techniques, subject's brain signals were measured before and after the relaxation exercises. We wish to determine if the relaxation exercise slowed the brain waves.

a) Matched pairs

b) One sample t test

c) Two sample t test

d) Two sample z test Question 5 To use the two sample t procedure to perform a significance test on the difference of two means, we assume:

a) The populations' standard deviation are known.

b) The samples from each population are independent.

c) The distributions are exactly normal in each population.

d) The sample sizes are large.

Question 6

Solid fats are more likely to raise blood cholesterol levels than liquid fats. Suppose a nutritionist analyzed the percentage of saturated fat for a sample of 6 brands of stick margarine (solid fat) and for a sample of 6 brands of liquid margarine and obtained the following results:

We want to determine if there a significant difference in the average amount of saturated fat in solid and liquid fats. What is the test statistic? (assume the population data is normally distributed)

a) t = 25.263

b) z = 39.604

c) t = 39.604

d) t = 39.104

e) z = 39.104

Question 7

It has been observed that some persons who suffer acute heartburn, again suffer acute heartburn within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug 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 first group and this group will be administered the new drug. There are 75 people in the second group and this



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group will be administered a placebo. After one year, 10% of the first group has a second episode and 9% of the 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 second episode 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 renal failure, again suffer renal failure within one year of the first episode. This is due, in part, to damage from the first episode. The performance of a new drug 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 31 people in the first group and this group will be administered the new drug. There are 45 people in the second group and this group will be administered a placebo. After one year, 11% of the first group has a second episode and 9% of the 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 second episode is more than 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 > 1.28, FRH0]

b) [z > -1.28 and z < 1.28, RH0]

c) [z < -1.28 and z > 1.28, FRH0]

d) [z < -1.28, FRH0]

e) [z < -1.28 or z > 1.28, RH0]

f) None of the above

Question 9

A private and a public university are located in the same city. For the private university, 1048 alumni were surveyed and 647 said that they attended at least one class reunion. For the public university, 797 out of 1319 sampled alumni claimed they have attended at least one class reunion. Is the difference in the sample proportions statistically significant? (Use =0.05)



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

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

c) There is not enough information to make a conclusion. 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 24 Yellow 21 Orange 13 Green 17 Blue 13

Using the 2 goodness of fit test to determine if the proportion of M&Ms is what is claimed, what is the test statistic?

a) 2 = 5.923 b) 2 = 5.423 c) 2 = 1.960 d) 2 = 11.847 e) 2 = 7.123

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:

Brown 23 Red 22 Yellow 21 Orange 12 Green 16 Blue 13



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Using the 2 goodness of fit test ( = 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 = 0.318, RH0] b) [p-value = 0.682, RH0] c) [p-value = 0.318, FRH0] d) [p-value = 0.159, RH0] e) [p-value = 0.682, FRH0] f) None of the above



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Quiz 14

Question 1

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

Hippocrates magazine states that 37 percent of all Americans take multiple vitamins regularly. Suppose a researcher surveyed 750 people to test this claim and found that 290 did regularly take a multiple vitamin. Is this sufficient evidence to conclude that the actual percentage is different from 37%?

a) One Sample Z Test for Proportions

b) 2 Goodness of Fit Test

c) Two Sample T Test for Means

d) 2 Test for Independence

e) Matched Pairs T Test

f) One Sample T Test for Means

g) Two Sample Z Test for Proportions

h) One Sample Z Test for Means Question 2 State the type of hypothesis test to be used in the following situation: Solid fats are more likely to raise blood cholesterol levels than liquid fats. Suppose a nutritionist analyzed the percentage of saturated fat for a sample of 6 brands of stick margarine (solid fat) and for a sample of 6 brands of liquid margarine and obtained the following results:

Stick 25.8 26.9 26.2 25.3 26.7 26.1 Liquid 16.9 17.4 16.8 16.2 17.3 16.8

Is there a significant difference in the average amount of saturated fat in solid and liquid fats? Assume the population is normally distributed.

a) Two Sample T Test for Means

b) 2 Goodness of Fit Test

c) Two Sample Z Test for Proportions



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d) 2 Test for Independence

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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 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 was chosen 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

Does there appear to be a relationship between gender and participation in the last election?

a) Two Sample Z Test for Proportions b) One Sample Z Test for Means c) 2 Test for Independence

d) One Sample Z Test for Proportions

e) One Sample T Test for Means

f) 2 Goodness of Fit Test

g) Two Sample T Test for Means

h) Matched Pairs T Test

Question 4

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

Men Women

Voted

2311 3422

Didn't Vote 1544 2723

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



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statistic?

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a) z = -20.564 b) 2 = 17.578 c) 2 = 26.367

d) z = -17.505

e) 2 = 15.789

Question 5

In a certain city, there are about one million eligible voters. A simple random sample of size 10,000 was chosen 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-value and 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% Brazil nuts, 20% almonds and only 25% peanuts. The truth-in-advertising investigators took a random sample (of size 20 lbs) of the nut mix and found the distribution to be as follows: 5 lbs of Cashews, 5 lbs of Brazil nuts, 8 lbs of Almonds and 2 lbs of Peanuts. At the 0.05 level of significance, is the claim made by Blue Diamond true? Select the [p-value, Decision to Reject (RH0) or Failure to Reject (FRH0)].

a) [p-value = 0.004, RH0]



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