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StatTutor Lesson - P-values and Statistical Significance

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      Question 1

      95

      Question 1.

      When do we have good evidence that a claim about a parameter is not true?

      A.
      B.

      Incorrect. We compute the probability on the statistic, not the parameter. So we have good evidence that the claim is not true when the probability on the statistic assuming the claim were true is really small.
      Correct. We compute the probability on the statistic, not the parameter. So we have good evidence that the claim is not true when the probability on the statistic assuming the claim were true is really small.
      Incorrect. Try again.
      2

      Question 2

      199

      Question 2.

      Suppose we are testing H0: µ = 50 versus Ha: µ > 50. What is the value of µ0?

      A.
      B.
      C.

      Incorrect. µ0 is the value given in the null hypothesis, so µ0 is 50.
      Correct. µ0 is the value given in the null hypothesis, so µ0 is 50.
      Incorrect. Try again.
      2

      Questions 3-4

      318

      Question 3.

      Why is a test statistic of z = 1.29 "not statistically significant?"

      A.
      B.

      Incorrect. When the value of a test statistic is likely to occur if the parameter claim were true, then the results are NOT statistically significant. A test statistic value of 1.29 is likely to occur because it is between -2 and +2.
      Correct. When the value of a test statistic is likely to occur if the parameter claim were true, then the results are NOT statistically significant. A test statistic value of 1.29 is likely to occur because it is between -2 and +2.
      Incorrect. Try again.
      2

      Questions 5-6

      382

      Question 5.

      Why is a test statistic value of z = 3.86 "statistically significant?"

      A.
      B.

      Incorrect. When the value of a test statistic is unlikely to occur if the parameter claim were true, then the results are statistically significant. A test statistic value of 3.86 is unlikely to occur because it is greater than +2.
      Correct. When the value of a test statistic is unlikely to occur if the parameter claim were true, then the results are statistically significant. A test statistic value of 3.86 is unlikely to occur because it is greater than +2.
      Incorrect. Try again.
      2

      Question 7

      445

      Question 7.

      True or false: The closer the observed statistic value is from the claimed parameter value, the more unlikely the statistic value is.

      A.
      B.

      Incorrect. Actually, the opposite is true. The farther the observed statistic value is from the claimed parameter value, the more unlikely the statistic value is.
      Correct. Actually, the opposite is true. The farther the observed statistic value is from the claimed parameter value, the more unlikely the statistic value is.
      Incorrect. Try again.
      2

      Questions 8-9

      499

      Question 8.

      What does "P" represent in "P-value?"

      A.
      B.
      C.

      Incorrect. To determine whether results are statistically significant, we need to find the probability of getting the observed statistic value. Thus, "P" represents "probability."
      Correct. To determine whether results are statistically significant, we need to find the probability of getting the observed statistic value. Thus, "P" represents "probability."
      Incorrect. Try again.
      2

      Question 10

      700

      Question 10.

      True or false: P-value is the probability of getting a sample mean value assuming the null hypothesis were true.

      A.
      B.

      Incorrect. P-value is the probability of getting a statistic assuming the null hypothesis were true. Actually, it is the probability of getting a statistic value as far or farther from that observed assuming the null hypothesis were true.
      Correct. P-value is the probability of getting a statistic assuming the null hypothesis were true. Actually, it is the probability of getting a statistic value as far or farther from that observed assuming the null hypothesis were true.
      Incorrect. Try again.
      2

      Question 11

      829

      Question 11.

      True or false: P-value is the probability that the null hypothesis were true.

      A.
      B.

      Incorrect. P-value is the probability of getting a statistic assuming the null hypothesis were true. Actually, it is the probability of getting a statistic value as far or farther from that observed assuming the null hypothesis were true. Note that the probability is on getting the statistic, not on the hypothesis.
      Correct. P-value is the probability of getting a statistic assuming the null hypothesis were true. Actually, it is the probability of getting a statistic value as far or farther from that observed assuming the null hypothesis were true. Note that the probability is on getting the statistic, not on the hypothesis.
      Incorrect. Try again.
      2

      Question 12

      863

      Question 12.

      True or false: The farther the value of ¯x is from the claimed value of µ on the sampling distribution of ¯x curve, the smaller the P-value.

      A.
      B.

      Incorrect. This is a correct statement.
      Correct. This is a correct statement.
      Incorrect. Try again.
      2

      Question 13

      1012

      Question 13.

      For what P-values do we reject H0?

      A.
      B.

      Incorrect. The rule is "P" low - reject H "oh."
      Correct. The rule is "P" low - reject H "oh."
      Incorrect. Try again.
      2

      Question 14

      1105

      Question 14.

      When are results "statistically significant?"

      A.
      B.

      Incorrect. We reject H0 and declare results to be "statistically significant" whenever P-value is small.
      Correct. We reject H0 and declare results to be "statistically significant" whenever P-value is small.
      Incorrect. Try again.
      2

      Questions 15-16

      1163

      Question 15.

      True or false: α is the symbol for level of significance.

      A.
      B.

      Incorrect. This is a correct statement.
      Correct. This is a correct statement.
      Incorrect. Try again.
      2

      Questions 17-18

      1306

      Question 17.

      If α = 0.10 and P-value = 0.236, can we reject H0?

      A.
      B.

      Incorrect. Since P-value = 0.236 is NOT less than α = 0.10, we cannot reject H0.
      Correct. Since P-value = 0.236 is NOT less than α = 0.10, we cannot reject H0.
      Incorrect. Try again.
      2

      Questions 19-20

      1357

      Question 19.

      If α = 0.05 and P-value = 0.017, can we reject H0?

      A.
      B.

      Incorrect. Since P-value = 0.017 is less than α= 0.05, we reject H0.
      Correct. Since P-value = 0.017 is less than α = 0.05, we reject H0.
      Incorrect. Try again.
      2

      Question 21

      1447

      Question 21.

      True or false: P-value is the probability that H0 is correct.

      A.
      B.

      Incorrect. P-value is the probability of getting a value of the test statistic assuming H0 were correct. It is a conditional probability - conditional on H0 being correct, not the probability that H0 is correct. Note that the probability is on the test statistic (or statistic), not H0.
      Correct. P-value is the probability of getting a value of the test statistic assuming H0 were correct. It is a conditional probability - conditional on H0 being correct, not the probability that H0 is correct. Note that the probability is on the test statistic (or statistic), not H0.
      Incorrect. Try again.
      2

      Question 22

      1519

      Question 22.

      When do we reject H0?

      A.
      B.

      Incorrect. We reject H0 whenever P-value is low; i.e., less than α.
      Correct. We reject H0 whenever P-value is low; i.e., less than α.
      Incorrect. Try again.
      2