Tests for a Population Mean

Tests for a population mean

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Questions 1-2

117

Question 1.

What should you conclude when P-value < α?

Conclude “insufficient evidence to believe H_a.”

Conclude H₀ is correct.

Conclude H_a is correct.

Incorrect. We have evidence to believe H_a when we reject H₀ and we reject H₀ when P-value < α.

Correct. We have evidence to believe H_a when we reject H₀ and we reject H₀ when P-value < α.

Incorrect. Try again.

Question 3

182

Question 3.

True or false: We assume H₀ is correct when computing P-value.

True

False

Incorrect. In using H₀ to specify the center of the sampling distribution of

$\overline{x}$ , we are assuming H₀ is correct.

Correct. In using H₀ to specify the center of the sampling distribution of

$\overline{x}$ , we are assuming H₀ is correct.

Incorrect. Try again.

Question 4

255

Question 4.

Which of the following hypotheses are two-sided?

H₀: μ = 16 versus H_a: μ ≠ 16

H₀: μ = 16 versus H_a: μ < 16

H₀: μ = 16 versus H_a: μ > 16

Incorrect. "≠” in H_a indicates that the hypotheses are two-sided.

Correct. "≠” in H_a indicates that the hypotheses are two-sided.

Incorrect. Try again.

Question 5

355

Question 5.

How do we know which tail of the sampling distribution of $\overline{x}$ contains the P-value of a test?

The tail containing P-value is specified by the direction in H_a.

The tail containing P-value is specified by the direction in H₀.

Incorrect. The direction in H_a tells us which tail contains the P-value for the test.

Correct. The direction in H_a tells us which tail contains the P-value for the test.

Incorrect. Try again.

Question 6

441

Question 6.

What is the appropriate alternative hypothesis for testing, “Is the mean for all BYU students less than 6?”

H_a: μ < 6

H_a: μ > 6

H_a: μ ≠ 6

Incorrect. The research question is “Is the mean for all BYU students less than 6?” So, H_a is “μ < 6.”

Correct. The research question is “Is the mean for all BYU students less than 6?” So, H_a is “μ < 6.”

Incorrect. Try again.

Questions 7-8

685

Question 7.

Why is P-value the area in the lower tail of the sampling distribution of $\overline{x}$ ?

Because we have “less than” (<) in H_a.

Because the test statistic is negative.

Because

$\overline{x}$ = 5.2 is less than μ = 6.

Incorrect. The direction specified in H_a tells us which tail in which to find P-value in the sampling distribution of

$\overline{x}$ .

Correct. The direction specified in H_a tells us which tail in which to find P-value in the sampling distribution of

$\overline{x}$ .

Incorrect. Try again.

Question 8.

When computing P-value of 0.0018, what did we compute the probability on?

On getting

$\overline{x}$ = 5.2 or lower

That μ = 6.

Incorrect. We computed the probability of getting

$\overline{x}$ = 5.2 or lower if μ = 6.

Correct. We computed the probability of getting

$\overline{x}$ = 5.2 or lower if μ = 6.

Incorrect. Try again.

Questions 9-10

691

Question 9.

For P-value = 0.0018 and α = 0.10, should we reject H₀?

Yes

Incorrect. Since P-value = 0.0018 is less than α = 0.10, we reject H₀.

Correct. Since P-value = 0.0018 is less than α = 0.10, we reject H₀.

Incorrect. Try again.

Question 11

703

Question 11.

Why did the data give “sufficient evidence” to conclude H_a was correct?

Because P-value was greater than α.

Because P-value was less than α.

Incorrect. Whenever P-value is less than α we have sufficience evidence to conclude H_a is correct.

Correct. Whenever P-value is less than α we have sufficience evidence to conclude H_a is correct.

Incorrect. Try again.

Question 12

823

Question 12.

What is the appropriate alternative hypothesis for testing, “Has the training raised the mean above 483?”

H_a: μ ≠ 483

H_a: μ < 483

H_a: μ > 483

Incorrect. The research question is “Has the training raised the mean above 483?” So, H_a is “μ > 483.”

Correct. The research question is “Has the training raised the mean above 483?” So, H_a is “μ > 483.”

Incorrect. Try again.

Questions 13-14

1063

Question 13.

Why is P-value the area in the upper tail of the sampling distribution of $\overline{x}$ ?

Because the test statistic is positive.

Because we have “greater than” (>) in H_a.

Because

$\overline{x}$ = 499.1 is greater than μ = 483.

Incorrect. The direction specified in H_a tells us which tail in which to find P-value in the sampling distribution of

$\overline{x}$ .

Correct. The direction specified in H_a tells us which tail in which to find P-value in the sampling distribution of

$\overline{x}$ .

Incorrect. Try again.

Question 14.

When computing P-value, what did we compute the probability on?

On getting

$\overline{x}$ = 499.1 or greater

That μ = 483.

Incorrect. We computed the probability of getting

$\overline{x}$ = 499.1 or greater if μ = 483.

Correct. We computed the probability of getting

$\overline{x}$ = 499.1 or greater if μ = 483.

Incorrect. Try again.

Questions 15-16

1078

Question 15.

For P-value = 0.2358 and α = 0.05, should we reject H₀?

Yes

Incorrect. Since P-value = 0.2358 is NOT less than α = 0.05, we do NOT reject H₀.

Correct. Since P-value = 0.2358 is NOT less than α = 0.05, we do NOT reject H₀.

Incorrect. Try again.

Question 17

1137

Question 17.

Why did the data give “insufficient evidence” to conclude H_a was correct?

Because P-value was greater than α.

Because P-value was less than α.

Incorrect. Whenever P-value is NOT less than α we have insufficience evidence to conclude H_a is correct.

Correct. Whenever P-value is NOT less than α we have insufficience evidence to conclude H_a is correct.

Incorrect. Try again.

Question 18

1224

Question 18.

What is the appropriate alternative hypothesis for testing, “Does the mean systolic blood pressure of all executives differ from 128?”

H_a: μ > 128

H_a: μ < 128

H_a: μ ≠ 128

Incorrect. The research question is “Does the mean differ from 128?” So, H_a is “μ ≠ 128.”

Correct. The research question is “Does the mean differ from 128?” So, H_a is “μ ≠ 128.”

Incorrect. Try again.

Question 19

1320

Question 19.

True or false: If the data were not collected with a simple random sample, the P-value computed from these data would be inaccurate.

True

False

Incorrect. If data are not appropriately collected, P-values and confidence levels are not accurate.

Correct. If data are not appropriately collected, P-values and confidence levels are not accurate.

Incorrect. Try again.

Question 20

1588

Question 20.

Why is P-value the area in both tails of the sampling distribution of $\overline{x}$ ?

Because we have “not equal to” (≠) in H_a.

Because the test statistic is negative.

Because

$\overline{x}$ = 126.07 is less than μ = 128.

Incorrect. The direction specified in H_a tells us which tail(s) in which to find P-value in the sampling distribution of

$\overline{x}$ . Since we have “≠” in H_a, we have a two-sided test and P-value is the area in both tails.

Correct. The direction specified in H_a tells us which tail(s) in which to find P-value in the sampling distribution of

$\overline{x}$ . Since we have “≠” in H_a, we have a two-sided test and P-value is the area in both tails.

Incorrect. Try again.

Questions 21-22

1605

Question 21.

For P-value = 0.2758 and α = 0.05, should we reject H₀?

Yes

Incorrect. Since P-value = 0.2758 is NOT less than α = 0.05, we do NOT reject H₀.

Correct. Since P-value = 0.2758 is NOT less than α = 0.05, we do NOT reject H₀.

Incorrect. Try again.

Question 23

1664

Question 23.

Why did the data give “insufficient evidence” to conclude H_a was correct?

Because P-value was greater than α.

Because P-value was less than α.

Incorrect. Whenever P-value is NOT less than α we have insufficience evidence to conclude H_a is correct.

Correct. Whenever P-value is NOT less than α we have insufficience evidence to conclude H_a is correct.

Incorrect. Try again.

Question 24

1772

Question 24.

True or false: P-value computation depends on the direction in the alternative hypothesis.

False

True

Incorrect. The direction in the alternative hypothesis specifies the tail (or tails) where we find the area of P-value.

Correct. The direction in the alternative hypothesis specifies the tail (or tails) where we find the area of P-value.

Incorrect. Try again.

StatTutor Lesson - Tests for a Population Mean

Questions 1-2

Question 1.

Question 2.

Question 3

Question 3.

Question 4

Question 4.

Question 5

Question 5.

Question 6

Question 6.

Questions 7-8

Question 7.

Question 8.

Questions 9-10

Question 9.

Question 10.

Question 11

Question 11.

Question 12

Question 12.

Questions 13-14

Question 13.

Question 14.

Questions 15-16

Question 15.

Question 16.

Question 17

Question 17.

Question 18

Question 18.

Question 19

Question 19.

Question 20

Question 20.

Questions 21-22

Question 21.

Question 22.

Question 23

Question 23.

Question 24

Question 24.