QUESTIONS

Question 1

Based on Hugo’s study outcomes regarding his pitch speed, choose the correct conclusions that interprets the results within the context of the hypothesis test. Select all that apply.

There is sufficient evidence at the 5%significance level to conclude that the mean speed is greater than 48 miles per hour.
There is NOT sufficient evidence 5%significance level to conclude that the mean speed is greater than 48 miles per hour.
This is a right-tailed test, and the test statistic is more than the critical value on the right side, so we reject the null hypothesis.
This is a right-tailed test, and the test statistic is less than the critical value on the left side, so we reject the null hypothesis.

Question 2

Based on the outcome of Huga’s test regarding is pitch speed, and the following results, conclude whether to reject or not reject H0.

H0: μ=48; Ha: μ>48
x¯=54
σ=5
α=0.05(significance level)
The test statistic is

z0 = x¯−μ0 /σ/√n

=54−48 / 5/√15

=4.65

The critical value is z₀₅=1.64.

Select two responses below.

Reject H0. At the 5%significance level, the data provide sufficient evidence to conclude that the mean speed is more than 48 miles per hour.
Fail to reject H0. At the 5%significance level, the test results are not statistically significant and at best, provide weak evidence against the null hypothesis.
The test statistic falls within the rejection region.
The test statistic is NOTin the rejection region.

Question 3

Hugo, a pitcher, estimates that his pitch speed is more than 48 miles per hour, on average. Several of his teammates would like his estimate to be tested, so he decides to do a hypothesis test, at a 5% significance level, to persuade them. He throws 15 pitches, collects the proper data, and works through the testing procedure:

H0: μ=48; Ha: μ>48
x¯=54
σ=5
α=0.05(significance level)
The test statistic is

z0 = x¯−μ0 / σ/√n

= 54−48 / 5/√15

=4.65

The critical value is z₀₅=1.64.

Conclude whether to reject or not reject H0, and interpret the results.

Based on this context and the null and alternative hypothesis, what type of hypothesis test should be used?

Use the curve below to show your answer. Select the appropriate test by dragging the blue point to a right-, left- or two-tailed diagram. The shaded area represents the rejection region. Then, set the critical value(s) on the x-axis by moving the purple slider on the right.

Question 4

Wrenley, a student midwife, predicts that the gestation periods among the population in her city are lower than the average 280 days due to pollution. She conducted a hypothesis test using a significance level of 5%.

Determine the critical value or values for a one-mean z-test at the 5% significance level if the hypothesis test is left-tailed (Ha:μ<μ0).

Z_0.10	Z_0.05	Z_0.025	Z_0.01	Z_0.005
1.285	1.645	1.960	2.326	2.576

Question 5

The mean math SAT score for seniors at Blue Moon High School is 560. An investigator believes that this score is different than the national average. After obtaining all relevant data, she conducted a hypothesis test using a significance level of 5%.

Determine the critical value or values for a one-mean z-test at the 5% significance level if the hypothesis test is two-tailed (Ha:μ≠μ₀).

Z_0.10	Z_0.05	Z_0.025	Z_0.01	Z_0.005
1.282	1.645	1.960	2.326	2.576

Question 6

Determine the critical value or values for a one-mean z-test at the 20% significance level if the hypothesis test is left-tailed (Ha:μ<μ0).

Z_0.8	Z_0.4	Z_0.2	Z_0.1	Z_0.005
-0.842	0.253	0.842	1.282	1.645

−1.282
−0.842
842
282
282and −1.282
842and −0.842

Question 7

Determine the critical value or values for a one-mean z-test at the 10% significance level if the hypothesis test is left-tailed (Ha: μ<μ0).

Z_0.10	Z_0.05	Z_0.025	Z_0.01	Z_0.005
1.282	1.645	1.960	2.326	2.576

−1.645
−1.282
282
645
645and −1.645
282and −1.282

Question 8

Based on your answers regarding the pharmacists results, choose the correct conclusion that interprets the results within the context of the hypothesis test.

There is sufficient evidence at the 10%significance level to conclude that the mean dosage is greater than 18
There is NOT sufficient evidence 10%significance level to conclude that the mean dosage is greater than 18
This is a right-tailed test, and test statistic is more than the critical value on the right side, so we reject the null hypothesis.
This is a right-tailed test, and test statistic is less than the critical value on the left side, so we reject the null hypothesis.

Question 9

Based on the results the pharmacist obtained from her hypothesis test and the following results, conclude whether to reject or not reject H0.

H0: μ=18; Ha: μ>18
x¯=19.1
Conclude whether to reject or not reject H0, and interpret the results
σ=1.6
α=0.1(significance level)
The test statistic is

z0 = x¯−μ0 / σ/√n

=19.1−18 / 1.6/√20

=3.07

The critical value is z₁=1.28.

Select two responses below.

Reject H0. The test statistic z0=3.07is greater than the critical value zα=1.28, for a right-tailed test and therefore there is enough evidence to reject H0 that the mean number of likes is not equal to 18mg per generic anti-histamine dose.
Fail to reject H0. The test statistic z0=3.07is greater than the critical value zα=1.28, for a right-tailed test and therefore there is NOT enough evidence to reject H0 that the mean number of likes is not equal to 18mg per generic anti-histamine dose.
The test statistic falls within the rejection region.
The test statistics is NOTin the rejection region.

Question 10

A pharmacist is researching the claim that a generic anti-histamine dose is more than 18 mg, on average. She decides to do a hypothesis test, at a 10% significance level. She measures 20 pills, collects the proper data, and works through the testing procedure:

H0: μ=18; Ha: μ>18
x¯=19.1
σ=1.6
α=0.1(significance level)
The test statistic is

z0 = x¯−μ0 / σ/√n

= 19.1−18 / 1.6/√20

=3.07

The critical value is z₁=1.28.

Conclude whether to reject or not reject H0, and interpret the results.

Based on this context and the null and alternative hypothesis, what type of hypothesis test should be used?

Question 11

Based on your answers above, choose the correct conclusion that interprets the results within the context of the hypothesis test.

There is sufficient evidence that the average annual credit card debt is greater than 8hundred dollars.
There is NOT sufficient evidence that the average annual credit card debt is greater than 8hundred dollars.
There is sufficient evidence that the average annual credit card debt is greater than 16hundred dollars.
There is NOT sufficient evidence that the average annual credit card debt is greater than 16hundred dollars.

Question 12

Based on your answer above, and the following results, conclude whether to reject or not reject H0.

H0: μ=16; Ha: μ>16
α=0.1(significance level)
The test statistic is 34.
The critical value is 1=1.28.

Select two responses below.

Reject H0.
Fail to reject H0.
The test statistic falls within the rejection region.
The test statistics is NOT in the rejection region.

Question 13

Suppose a financial adviser would like to make the claim that his clients pay annual credit card interest that is more than 16 hundred dollars, on average. Several of his customers do not believe him, so the financial adviser decides to do a hypothesis test, at a 10% significance level, to persuade them. He conducts a financial analysis on 21 of his customers and calculates the sample average to be 17.8 hundred dollars. Working through the testing procedure:

H0: μ=16; Ha: μ>16
α=0.1(significance level)
The test statistic is

z0 = x¯−μ0 / σ/√n

=17.8−16 / 1.3/√21

=6.34

The critical value is z₁=1.28.

Based on this context and the null and alternative hypothesis, what type of hypothesis test should be used?

ANSWERS:

Question 1

Based on Hugo’s study outcomes regarding his pitch speed, choose the correct conclusions that interprets the results within the context of the hypothesis test. Select all that apply.

There is sufficient evidence at the 5%significance level to conclude that the mean speed is greater than 48 miles per hour.
There is NOT sufficient evidence 5%significance level to conclude that the mean speed is greater than 48 miles per hour.
This is a right-tailed test, and the test statistic is more than the critical value on the right side, so we reject the null hypothesis.
This is a right-tailed test, and the test statistic is less than the critical value on the left side, so we reject the null hypothesis.

Answer

There is sufficient evidence at the 5% significance level to conclude that the mean speed is greater than 48 miles per hour.

Question 2

Based on the outcome of Huga’s test regarding is pitch speed, and the following results, conclude whether to reject or not reject H0.

H0: μ=48; Ha: μ>48
x¯=54
σ=5
α=0.05(significance level)
The test statistic is

z0 = x¯−μ0 /σ/√n

=54−48 / 5/√15

=4.65

The critical value is z₀₅=1.64.

Select two responses below.

Reject H0. At the 5%significance level, the data provide sufficient evidence to conclude that the mean speed is more than 48 miles per hour.
Fail to reject H0. At the 5%significance level, the test results are not statistically significant and at best, provide weak evidence against the null hypothesis.
The test statistic falls within the rejection region.
The test statistic is NOTin the rejection region.

Answer

Reject H0. At the 5% significance level, the data provide sufficient evidence to conclude that the mean speed is more than 48 miles per hour.

…

Question 3

H0: μ=48; Ha: μ>48
x¯=54
σ=5
α=0.05(significance level)
The test statistic is

z0 = x¯−μ0 / σ/√n

= 54−48 / 5/√15

=4.65

The critical value is z₀₅=1.64.

Conclude whether to reject or not reject H0, and interpret the results.

Based on this context and the null and alternative hypothesis, what type of hypothesis test should be used?

Answer

This is a right-tailed test, because Ha states the pitch speed is more than 48 miles per hour, on average. “More than” refers to a greater than inequality, which is a right-tailed test.

The critical value is z_0.1=1.64

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(Answer) MATH399N – Week 7 Assignment: Conduct a Hypothesis Test for Mean – Population Standard Deviation Known – Critical Value/Rejection Region Approach