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Question 13 (1 point) A statistics professor wants to examine the number of hours that seniors...

Question 13 (1 point)

A statistics professor wants to examine the number of hours that seniors and freshmen study for the final. Specifically, the professor wants to test if the average number of hours that seniors study is greater than the average number of hours that freshmen study. If the seniors are considered group 1 and the freshmen are considered group 2, what are the hypotheses for this scenario?

Question 13 options:

1)

HO: μ1 = μ2
HA: μ1 ≠ μ2

2)

HO: μ1 ≤ μ2
HA: μ1 > μ2

3)

HO: μ1 > μ2
HA: μ1 ≤ μ2

4)

HO: μ1 ≥ μ2
HA: μ1 < μ2

5)

HO: μ1 < μ2
HA: μ1 ≥ μ2

Question 14 (1 point)

Does the amount of hazardous material absorbed by the bodies of hazardous waste workers depend on gender? You want to test the hypotheses that the amount absorbed by men (group 1) is greater than the amount absorbed by women (group 2). A random sample of 286 male workers and 168 female workers showed an average lead absorption in the blood of 14.84 (SD = 1.163) and 14.75 (SD = 0.976), respectively (measured in micrograms/deciliter). Assuming that the population standard deviations are the same, perform a two independent samples t-test on the hypotheses Null Hypothesis: μ1 ≤ μ2, Alternative Hypothesis: μ1 > μ2. What is the test statistic and p-value of this test?

Question 14 options:

1)

Test Statistic: -0.844, P-Value: 0.1996

2)

Test Statistic: 0.844, P-Value: 0.3992

3)

Test Statistic: -0.844, P-Value: 0.8004

4)

Test Statistic: 0.844, P-Value: 0.8004

5)

Test Statistic: 0.844, P-Value: 0.1996

Question 15 (1 point)

The owner of a local golf course wants to examine the difference between the average ages of males and females that play on the golf course. Specifically, he wants to test if the average age of males is different from the average age of females. If the owner conducts a hypothesis test for two independent samples and calculates a p-value of 0.9205, what is the appropriate conclusion? Label males as group 1 and females as group 2.

Question 15 options:

1)

The average age of males is significantly different from the average age of females.

2)

We did not find enough evidence to say a significant difference exists between the average age of males and females.

3)

We did not find enough evidence to say the average age of males is larger than the average age of females.

4)

The average age of males is equal to the average age of females.

5)

We did not find enough evidence to say the average age of males is less than the average age of females.

Question 16 (1 point)

The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in high-crime areas of Miami, Florida, are being examined to test the effectiveness of the program. The difference in crimes reported is calculated as (crimes after - crimes before). You want to test whether the crimes reported after is different from those reported before and, thus, the hypotheses are as follows: Null Hypothesis: μD = 0, Alternative Hypothesis: μD ≠ 0. You perform a paired sample t-test and see a p-value of 0.0018. What is the appropriate conclusion?

Question 16 options:

1)

The average difference in crimes reported is significantly different from 0. There is a significant difference in crimes reported due to the program.

2)

The average difference in crimes reported is significantly less than 0. The average number of crimes reported was higher before the program.

3)

We did not find enough evidence to say the average difference in crimes reported was not 0. The program does not appear to have been effective.

4)

The average difference in crimes reported is equal to 0.

5)

The average difference in crimes reported is significantly larger than 0. The average number of crimes reported was higher after the program.

Question 17 (1 point)

In the year 2000, the average car had a fuel economy of 20.9 MPG. You are curious as to whether the average in the present day is less than the historical value. The hypotheses for this scenario are as follows: Null Hypothesis: μ ≥ 20.9, Alternative Hypothesis: μ < 20.9. If the true average fuel economy today is 22.1 MPG and the null hypothesis is not rejected, did a type I, type II, or no error occur?

Question 17 options:

1)

Type II Error has occurred

2)

We do not know the degrees of freedom, so we cannot determine if an error has occurred.

3)

Type I Error has occurred.

4)

We do not know the p-value, so we cannot determine if an error has occurred.

5)

No error has occurred.

Homework Answers

Answer #1

13)

option 2 is correct

14)

Pooled Std dev Sp=√((n1-1)s21+(n2-1)*s22)/(n1+n2-2)= 1.0976
Point estimate : x1-x2= 0.0900
standard error se =Sp*√(1/n1+1/n2)= 0.107
test stat t =(x1-x2-Δo)/Se= 0.844
p value : = 0.1997

option 5

15)

We did not find enough evidence to say a significant difference exists between the average age of males and females

16)since p value <0.05

The average difference in crimes reported is significantly different from 0. There is a significant difference in crimes reported due to the program.

17)since null is correct and we did not reject

No error has occurred.

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