Question

Please show work/explain on each question:

1.According to a recent census, 15% of the people in the United States are of Hispanic origin. One county supervisor believes her county has a lower proportion of Hispanic people than the nation as a whole. She looks at their most recent survey data, which was a random sample of 485 county residents, and found that 43 of those surveyed are of Hispanic origin. Calculate the test statistic Z.

Group of answer choices

3.64

-4.56

-3.78

-3.01

2.

According to a recent census, 14% of the people in the United States are of Hispanic origin. One county supervisor believes her county has a different proportion of Hispanic people than the nation as a whole. She looks at their most recent survey data, which was a random sample of 460 county residents, and found that 42 of those surveyed are of Hispanic origin. Test statistic Z is found to be -3.01. Use α = 0.01. State the conclusion.

Group of answer choices

Do not Reject Ho, There is not sufficient evidence that the Hispanic population in this county differs from that of the nation as a whole.

Reject Ho. There is not sufficient evidence that the Hispanic population in this county differs from that of the nation as a whole.

Reject Ho.There is evidence that the Hispanic population in this county differs from that of the nation as a whole.

Do not Reject Ho. There is evidence that the Hispanic population in this county differs from that of the nation as a whole.

3.

If Test statistic Z is found to be 1.01 and HA: p > 0.09, what is P-value?

Group of answer choices

0.0000

0.1562

0.0131

0.0035

4.

In 1960, census results indicated that the age at which men in a certain region first married had a mean of 24.2 years. We want to find out if the mean age of first marriage has decreased from 24.2 years since then (µ < 24.2) . The 40 men in our sample first married at an average age of 23.2 years, with a sample standard deviation s of 5.4 years. The test statistic t is -1.171. Then, P-value is __________________.

Group of answer choices

P(t = -1.171)

P(t<-1.171)

P(t > 1.171)x2

P(t ≠ 1.171)

5.

In 1960, census results indicated that the age at which men in a certain region first married had a mean of 24.5 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has increased from 24.5 years since then (µ > 24.5). The 40 men in our sample first married at an average age of 25.4 years, with a sample standard deviation s of 5.3 years. The P-value is 0.145. State the conclusion using α = 0.01.

Group of answer choices

Reject Ho. There is not sufficient evidence that the mean age of first marriage differs from the mean age in 1960.

Do not Reject Ho. There is sufficient evidence that the mean age of first marriage is greater than the mean age in 1960.

Reject Ho. There is sufficient evidence that the mean age of first marriage is greater than the mean age in 1960.

Do not Reject Ho. There is not sufficient evidence that the mean age of first marriage is greater than the mean age in 1960.

6.

In 1960, census results indicated that the age at which men in a certain region first married had a mean of 23.5 years. We want to find out if the mean age of first marriage has changed/differed from 23.5 years since then. The 40 men in our sample first married at an average age of 24.3 years, with a sample standard deviation s of 5.3 years. Calculate the test statistic t.

Group of answer choices

1.171

1.074

0.955

0.145

7.

Ahmadi, Inc. has been manufacturing small automobiles that have averaged 50 miles per gallon of gasoline in highway driving. The company has developed a more efficient engine for its small cars and now advertises that its new small cars average more than 50 miles per gallon in highway driving. An independent testing service road-tested 64 of the new small automobiles. The sample showed an average of 51.5 miles per gallon. The population standard deviation is 4 miles per gallon.

Ahmadi, Inc wants to conduct a hypothesis test to determine whether or not it is legitimate campaign that the new small cars average more than 50 miles per gallon in highway driving. Use α = 0.05

What type of the test is appropriate?

Group of answer choices

No answer text provided.

t-test for one population mean

z-test for one population proportion

z-test for one population mean

Answer 1

Solution:

a) Given

n = 485 sample size of Hispanic origin.

X = 43

p = 0.15 population proportion of Hispanic origin.

q =1- p = 0.85

sample proportion of Hispanic origin

Test statistic

Z = - 3.783868

Test statistic Z = -3.78

Option C is correct

2 )

To test

. Vs.

Test statistic Z = - 3.01 given

At level of significance

from Z table

The Z critical value = 2.58

3.01 > 2.58

Reject Ho.

Conclusion: There is sufficient evidence that the the Hispanic population in the County difference from that of the nation as a whole .

Option C is correct

3) To test

Ho : p = 0.09 vs. Ha : p > 0.09

Test statistic Z = 1.01

P Value = 0.1562 from Z table.

Option B is correct

4 ) To test

. Vs.   

Test statistic t = -1.171

P Value

P ( t < -1.171) = 0.124352

P Value = 0.124352 from online P value calculator

Option B is correct

5) To test

. Vs.

P Value = 0.145

level of significance

Decision : P value

Fail to reject Ho

Conclusion : Do not reject Ho, There is insufficient evidence to conclude that the mean age of first marriage is greater than the mean age in 1960.

Option D is correct.

6) Given

n= 40 sample size

population mean

sample mean

s = 5.3 sample standard deviations

To test

. Vs.

Test statistic

t = 0.9546496

Test statistic t = 0.955

Option C is correct.

7) Z test for one population mean is used for testing this hypothesis, because the sample size n=64 >30 also the population standard deviations is known to us.

Hence we used one sample Z test for population mean.