If a court acquits every defendant, they will never commit a Type I error.
A) True
B) False
2.
The probability of rejecting a true null hypothesis increases as the sample size increases.
A) True
B) False
3.
For a given level of significance, the critical value of Student's t increases as n increases.
A) True
B) False
4.
In a two-tailed hypothesis test with á = .05, a test statistic of t = 1.813 with d.f. = 15 leads one to reject the null hypothesis of a statistical test.
A) True
B) False
5.
The power of a test is the probability that the test will reject a false null hypothesis.
A) True
B) False
6.
The height of the power curve shows the probability of accepting a true null hypothesis
A) True
B) False
7.
Which is not true of p-values?
A) When they are small, we want to reject Ho.
B) They must be specified before the sample is taken.
C) They show the chance of Type I error if we reject Ho.
D) They do not require á to be specified a priori.
Use the following scenario to answer questions 8 to 10.
Dullco Manufacturing claims that its alkaline batteries last forty hours on average in a certain type of portable CD player. Tests on a random sample of 18 batteries showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours.
8.
The test statistic is
A) -1.980
B) -1.728
C) -2.101
D) -1.960
9.
In determining the p-value for reporting the study's findings, which of the following is true?
A) The p-value is less than .05.
B) The p-value is equal to .05.
C) The p-value is greater than .05.
D) The p-value cannot be determined without specifying á.
10.
In a left-tailed test at á = .05 we would
A) comfortably reject the claim.
B) comfortably accept the claim.
C) feel uncomfortable with either decision (too close).
D) switch to alpha of 0.01 for a more powerful test.
--------------------------------------------------------------------------------
Use the following scenario to answer questions 11 to 13.
A TV special said there is a 10 per cent incidence of sexually transmitted disease (STD) among all U.S. teens. A reporter for the Rockville Bugle, looking for a story, surveyed 260 randomly chosen teenagers, and found that 39 had been to a clinic for STD treatment. Use a right-tail test at á = .05.
11.
The test statistic is
A) 2.687
B) 2.758
C) .0256
D) 2.258
12.
The critical value is
A) 1.645
B) 1.658
C) 1.697
D) 1.960
13.
The p-value is
A) .0501
B) .0314
C) 2.258
D) .0036
14.
Which of the following statements is correct?
A) For a given level of significance, the critical value of Student's t increases as n increases.
B) A test statistic of t = 2.131 with d.f. = 15 leads to a clear-cut decision in a two-tailed test where á = .05.
C) It is harder to reject the null hypothesis when conducting a two-tailed test rather than a one-tailed test.
D) If we desire á = 0.10 then a p-value of 0.13 would lead us to reject the null hypothesis.
15.
John rejected a null hypothesis in a right-tailed test for a mean at á = .025 because his critical t value was 2.000 and his calculated t value was 2.345. We can be sure that
A) John did not commit Type I error.
B) John did not commit Type II error.
C) John committed neither Type I nor Type II error.
D) none of the above can definitely be concluded.
The very least you should learn from the study of a subject is how to spell it. These questions are about statistics. "Statics" is a topic in basic civil engineering (mechanics of non-moving rigid bodies).
Dullco Manufacturing claims that its alkaline batteries last forty hours on average in a certain type of portable CD player.
what are the answers for questions 1-12
In a left-tailed test at á = .05 we would
A) comfortably reject the claim.
B) comfortably accept the claim.
C) feel uncomfortable with either decision (too close).
D) switch to alpha of 0.01 for a more powerful test.
4. a
5.b
6.b
7.d
a
a
b
a
c
1. B) False. If a court acquits every defendant, it means that they are not finding any defendants guilty, regardless of whether they are actually innocent or guilty. This means that they can potentially be committing Type II errors, where they are failing to reject a false null hypothesis (in this case, the null hypothesis being that the defendant is innocent).
2. A) True. The probability of rejecting a true null hypothesis, also known as a Type I error, increases as the sample size increases. This is because a larger sample size provides more evidence and reduces the likelihood of making a false rejection.
3. B) False. For a given level of significance, the critical value of Student's t does not necessarily increase as n increases. The critical value depends on the degrees of freedom (df), which is related to the sample size (n) and the specific test being conducted. In some cases, as the sample size increases, the critical value may remain the same or even decrease.
4. B) False. In a two-tailed hypothesis test with α = .05, a test statistic of t = 1.813 with df = 15 does not lead to rejecting the null hypothesis. The critical value for a two-tailed test with α = .05 and df = 15 is approximately ±2.131. Since |1.813| < 2.131, the null hypothesis would not be rejected.
5. A) True. The power of a test is the probability that the test will correctly reject a false null hypothesis, or in other words, the probability of detecting an effect when it truly exists. It is the complement of Type II error (β).
6. B) False. The height of the power curve shows the probability of rejecting a false null hypothesis, not accepting a true null hypothesis. The power curve represents the relationship between the effect size and the probability of rejecting the null hypothesis.
7. D) They do not require α to be specified a priori. This statement is not true of p-values. p-values reflect the probability of obtaining the observed sample results (or more extreme results) under the assumption that the null hypothesis is true. They do not depend on the significance level (α) specified for the test.
8. C) -2.101. The test statistic can be calculated using the formula: (sample mean - population mean) / (sample standard deviation / √sample size). In this case, the test statistic is (37.8 - 40) / (5.4 / √18) = -2.101.
9. C) The p-value is greater than .05. The p-value represents the probability of obtaining the observed sample results (or more extreme results) under the assumption that the null hypothesis is true. If the p-value is greater than .05, it means that the observed data is not statistically significant at the 5% level and we would fail to reject the null hypothesis.
10. C) Feel uncomfortable with either decision (too close). In a left-tailed test at α = .05, if the test statistic falls just below the critical value and the p-value is slightly above .05, it would indicate that the decision is too close to comfortably reject the claim or accept the claim. In such cases, further investigation or a larger sample size may be needed for a more conclusive decision.
11. A) 2.687. The test statistic can be calculated using the formula: (sample proportion - population proportion) / √((population proportion * (1 - population proportion)) / sample size). In this case, the sample proportion is 39/260 = 0.15 and the population proportion is 0.10. Plugging in the values, we get (0.15 - 0.10) / √((0.10 * 0.90) / 260) = 2.687.
12. A) 1.645. The critical value represents the threshold beyond which we reject the null hypothesis. In a right-tailed test at α = .05, the critical value corresponds to the z-score that leaves a tail probability of 0.05 (or 5%) in the right tail of the standard normal distribution. In this case, the critical value is 1.645.
13. B) .0314. The p-value represents the probability of obtaining the observed sample results (or more extreme results) under the assumption that the null hypothesis is true. In this case, the observed test statistic (2.758) corresponds to a p-value of 0.0314, which is less than .05. Therefore, we would reject the null hypothesis.
14. A) For a given level of significance, the critical value of Student's t increases as n increases. This statement is true. As the sample size (n) increases, the degrees of freedom (df) increase, which affects the critical value of Student's t. With more degrees of freedom, the critical t value increases, providing a narrower rejection region and making it harder to reject the null hypothesis.
15. D) None of the above can definitely be concluded. From the information given, we cannot definitively conclude whether John committed a Type I error, Type II error, or neither. The conclusion depends on the specific hypothesis being tested, the chosen significance level (α), and the actual values of the critical t value and the calculated t value.