Question

A team of researchers would like to find out if Country X residents, who favor a low fat diet, have significantly lower cholesterol levels compared to that of the US population. They collected data from a large sample of Country X residents and the Z statistic is calculated to be -1.34 in a one-tailed test with an alpha level of .05. What is the researchers' conclusion of the hypothesis test?

Group of answer choices

The researchers fail to reject the null hypothesis.

The researchers reject the alternative hypothesis.

The researchers reject the null hypothesis.

More information is needed to reach a conclusion.

A study was conducted on the effect of money on life satisfaction by comparing a group of people who are financially wealthy to the general population. Based on the statistical result, the researchers failed to reject the null hypothesis, so it can be concluded that ____.

Group of answer choices

the probability is high that the life satisfaction of people who are wealthy is different from the general population

life satisfaction of people who are wealthy has been proven to be the same as the general population

life satisfaction of people who are wealthy has been proven to be different from the general population

the probability is high that the life satisfaction of people who are wealthy is the same as the general population

Based on the national statistics on MPG ratings, the national average rating for sedans is 25 with a standard deviation of 5. My car has an MPG of 29, what is the percentage of sedans performing better than my car in MPG?

Group of answer choices

50 + 28.81% - 78.81%

50% - 28.81% = 21.19%

100% - 34.13% = 65.87%

100% - 34.13% = 65.86%

When using the Z table for a two-tailed hypothesis test with a preset alpha (significance) level, what is the correct sequence of the following steps (it is possible not all steps will be used):

1) Look for the corresponding Z value(s)
2) Multiply the percentage of alpha by 2 to be the "tail area percentage"
3) Look in the "tail" column for the "tail area percentage”
4) Divide the percentage of alpha by 2 to be the "tail area percentage"
5) Convert the alpha to percentage

Group of answer choices

5, 4, 3, 1

5, 2, 3, 1

5, 4, 3, 1, 2

1, 2, 3

How does a two-tailed test compared to a one-tailed test when given a sample statistic and a fixed alpha level?

Group of answer choices

The critical value to be compared to the statistic would be less extreme with a two-tailed test.

The critical value to be compared to the statistic would be more extreme with a two-tailed test.

The total significance area in the comparison distribution is larger in a two-tailed test.

The total significance area in the comparison distribution is smaller in a one-tailed test.

Answer 1

1. A team of researchers would like to find out if Country X residents, who favor a low fat diet, have significantly lower cholesterol levels compared to that of the US population. They collected data from a large sample of Country X residents and the Z statistic is calculated to be -1.34 in a one-tailed test with an alpha level of .05. What is the researchers' conclusion of the hypothesis test?

Let

• \mu_{X} : Mean Cholestrol levels of the residents of country X
• \mu_{us}: Mean Cholestrol levels of the residents of US

Stating the hypothesis

Obtained test statistic:

The corresponding  

Since the test is one-tailed, carried out at level of significance and
the  ,

We don't have sufficient evidence to reject the null.
So the correct option is The researchers fail to reject the null hypothesis.

2. A study was conducted on the effect of money on life satisfaction by comparing a group of people who are financially wealthy to the general population. Based on the statistical result, the researchers failed to reject the null hypothesis, so it can be concluded that ____.

H_{0}: life satisfaction of people who are wealthy is the same as the general population
(i.e. money has no effect on the life satisfaction of people)

H_{a}: life satisfaction of people who are wealthy is different from the general population
(i.e. money has some effect on the life satisfaction of people)

since the researchers failed to reject the null hypothesis, this implies they did not find sufficient evidence to support the claim that money has an effect on the life satisfaction of people.
So the correct option is the probability is high that the life satisfaction of people who are wealthy is the same as the general population

3. Based on the national statistics on MPG ratings, the national average rating for sedans is 25 with a standard deviation of 5. My car has an MPG of 29, what is the percentage of sedans performing better than my car in MPG?

Let the random variable = The MPG rating of a sedan
Assume that X is normally distributed ,  

The Z-score of the car having an MPG of 29 is:

The percentage of cars performing better than the car having an MPG rating of 29 is:

Hence the correct answer is 50% - 28.81% = 21.19%

4. When using the Z table for a two-tailed hypothesis test with a preset alpha (significance) level, what is the correct sequence of the following steps (it is possible not all steps will be used):

1) Look for the corresponding Z value(s)
2) Multiply the percentage of alpha by 2 to be the "tail area percentage"
3) Look in the "tail" column for the "tail area percentage”
4) Divide the percentage of alpha by 2 to be the "tail area percentage"
5) Convert the alpha to percentage

The correct choice is 5, 4, 3, 1

5. How does a two-tailed test compared to a one-tailed test when given a sample statistic and a fixed alpha level?

The correct choice is The critical value to be compared to the statistic would be more extreme with a two-tailed test

Here the critical value for the Two-tailed test = 1.96 is more extreme (greater)
than the critical value for the One-tailed test = 1.645