Exam 4 (chap 17 and hypoth test portions of 18, 20)

A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2 hypertension. If the diet is effective, the target is to have the average systolic blood pressure of this group be below 150. After six months on the diet, an SRS of 28 patients had an average systolic blood pressure of = 143, with standard deviation s = 21. Is this sufficient evidence that the diet is effective in meeting the target? Assume that the distribution of the systolic blood pressure for patients in this group is approximately Normal with mean μ. Based on the data, the value of the one-sample t statistic is:

-1.76.

Suppose we are testing the null hypothesis H0: μ = 20 and the alternative Ha: μ 20, for a normal population with σ = 5. A random sample of 25 observations are drawn from the population, and we find the sample mean of these observations is = 17.6. The P-value is closest to: a. .1336. b. 0.0082. c. 0.0668. d. .0164.

.0164.

A statistician wishing to test a hypothesis that students score at least 75% on the final exam in an introductory statistics course decides to randomly select 20 students in the class and have them take the exam early. The average score of the 20 students on the exam was 78% and the standard deviation in the population is known to be σ = 15%. The P-value for the hypothesis H0: μ = 75 vs. Ha: μ > 75 is: a. 0.186. b. 0.371. c. 0.814. d. The answer cannot be determined with information provided.

0.186.

A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2 hypertension. If the diet is effective, the target is to have the average systolic blood pressure of this group be below 150. After six months on the diet, an SRS of 28 patients had an average systolic blood pressure of = 143, with standard deviation s = 21. Is this sufficient evidence that the diet is effective in meeting the target? Assume that the distribution of the systolic blood pressure for patients in this group is approximately Normal with mean μ. The appropriate degrees of freedom for this test are: 27. 149. 28. 20.

27

Suppose the time that it takes a certain large bank to approve a home loan is Normally distributed with mean (in days) μ and standard deviation σ = 1. The bank advertises that it approve loans in 5 days, on average, but measurements on a random sample of 500 loan applications to this bank gave a mean approval time of = 5.3 days. Is this evidence that the mean time to approval is actually longer than advertised? To answer this, test the hypotheses H0: μ = 5, Ha: μ > 5 at significance level α = 0.01. You conclude that: a. H0 should be rejected. b. H0 should not be rejected. c. Ha should be rejected. d. there is a 5% chance that the null hypothesis is true.

H0 should be rejected.

The mean area μ of the several thousand apartments in a new development by a certain builder is advertised to be 1100 square feet. A tenant group thinks this is inaccurate, and suspects that the actual average area is less than 1100 square feet. In order to investigate this suspicion, the group hires an engineer to measure a sample of apartments to verify its suspicion. The appropriate null and alternative hypotheses, H0 and Ha, for μ are: a. H0: μ = 1100 and Ha: μ < 1100. b. H0: μ = 1100 and Ha: μ 1100. c. The hypotheses cannot be specified without knowing the size of the sample used by the engineer. d. H0: μ = 1100 and Ha: μ > 1100.

H0: μ = 1100 and Ha: μ < 1100.

A statistician wishing to test a hypothesis that students score at least 75% on the final exam in an introductory statistics course decides to randomly select 20 students in the class and have them take the exam early. The average score of the students on the exam was 78%. The hypothesis the statistician wants to test is:

H0: μ = 75 vs. Ha: μ > 75.

In their advertisements, the manufacturers of a certain brand of breakfast cereal would like to claim that eating their oatmeal for breakfast daily will produce a mean decrease in cholesterol of more than 10 points in one month for people with cholesterol levels over 200. In order to determine if this is a valid claim, they hire an independent testing agency, which then selects 25 people with a cholesterol level over 200 to eat their cereal for breakfast daily for a month. The agency should be testing the null hypothesis H0: μ = 10 and the alternative hypothesis:

Ha: μ >10.

3. Which is an acceptable statement of a null and alternative hypothesis about a mean?

None of the above

If a hypothesis test is significant at level α = 0.05, then what is known for the P-value?

P-value ≤ 0.05

A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2 hypertension. If the diet is effective, the target is to have the average systolic blood pressure of this group be below 150. After six months on the diet, an SRS of 28 patients had an average systolic blood pressure of = 143, with standard deviation s = 21. Is this sufficient evidence that the diet is effective in meeting the target? Assume that the distribution of the systolic blood pressure for patients in this group is approximately Normal with mean μ. Given a P-value between 0.01 and 0.05, what conclusion should you draw at the 5% level of significance?

Reject the null hypothesis because the P-value is less than the level of significance.

A researcher wishes to determine if the use of an herbal extract improves memory. Subjects will take the herbal extract regularly during a 10-week period of time. After this course of treatment, each subject has his or her memory tested using a standard memory test. Suppose the scores on this test of memory for all potential subjects taking the herbal extract follow a Normal distribution with mean μ and standard deviation σ = 6. Suppose also, that in the general population of all people, scores on the memory test follow a Normal distribution, with mean 50 and standard deviation σ = 4. The researcher, therefore, decides to test the hypotheses H0: μ = 50, Ha: μ > 50 To do so, the researcher has 100 subjects follow the protocol described above. The mean score for these students is = 55.2 and the P-value is less than 0.0001. Which statement is an appropriate to conclusion? a . None of the above b. The researcher has strong evidence that use of this herbal supplement improves memory, and because the P-value is so small, the difference must be substantial. c. The researcher has strong evidence that people that use this herbal extract, on average, have higher memory test scores than those that don't use this extract. However, the difference may or may not be important. d. The researcher has conclusively proved that use of this herbal extract improves memory.

The researcher has strong evidence that people that use this herbal extract, on average, have higher memory test scores than those that don't use this extract. However, the difference may or may not be important.

I read an article about a new drug which stated that "the incidence of side effects was similar to placebo, P-value > 0.05." I want to know if the results are significant at 10%. With the information given,

There is not enough information given to make a conclusion.

In a test of hypothesis, a small P-value provides evidence: a. against the null hypothesis in favor of the alternative hypothesis. b. against the null hypothesis and the alternative hypothesis. c. against the alternative hypothesis in favor of the null hypothesis. d. for the null and the alternative hypothesis.

a. against the null hypothesis in favor of the alternative hypothesis.

The P-value measures the strength of evidence: a. sometimes against the null hypothesis and sometimes against the alternative hypothesis. b. against the null hypothesis. c.the interpretation depends on whether we reject the null hypothesis. d.against the alternative hypothesis.

b. against the null hypothesis.

In a statistical test of hypotheses, we say the data are statistically significant at level α if: a. α = 0.05. b. the P-value is less than α. c. α is small. d. the P-value is larger than α.

b. the P-value is less than α.

Which question can be used to draw conclusions from a test of significance? a. If <i>p</i> is greater than the significance level &#945;, then reject the null hypothesis. b. If the <i>P</i>-value is greater than the significance level &#945;, then reject the null hypothesis. c. If the <i>P</i>-value is less than the significance level &#945;, then reject the null hypothesis. d. If <i>p</i> is less than the significance level &#945;, then reject the alternative hypothesis.

c. If the <i>P</i>-value is less than the significance level &#945;, then reject the null hypothesis.

You conduct a statistical test of hypotheses and find that the null hypothesis is statistically significant at level α = 0.05. You may conclude that the test would also be significant at: a. both level α = 0.10 and level α = 0.01. b.None of the above c.level α = 0.10. d.level α = 0.01.

c. level α = 0.10

Suppose the weights of 7th graders at a certain school vary according to a normal distribution with a mean of 100 pounds and a standard deviation of 7.5 pounds. A researcher believes the average weight has decreased since the implementation of a new breakfast and lunch program at the school. For a test of significance, state the alternative hypothesis. a. μ = 100 b. μ > 100 {b. is incorrect. The alternative hypothesis is the one researchers are looking for evidence of and they are looking for evidence the true mean has decreased. Text reference: section 17.2} c. μ < 100 d. μ ≠ 100

c. μ < 100

The time (in number of days) until maturity of a certain variety of tomato plant is Normally distributed with mean μ and standard deviation σ = 2.4. I select a simple random sample of four plants of this variety and measure the time until maturity. The sample yields = 65. You read on the package of seeds that these tomatoes reach maturity, on average, in 61 days. You want to test to see if your seeds are reaching maturity later than expected, which might indicate that your package of seeds is too old. The appropriate hypotheses are: a. H0: μ = 65, Ha: μ > 65. b. H0: μ = 65, Ha: μ < 65. c. H0: μ = 61, Ha: μ < 61. d. H0: μ = 61, Ha: μ > 61.

d. H0: μ = 61, Ha: μ > 61.

A special diet is intended to reduce systolic blood pressure among patients diagnosed with stage 2 hypertension. If the diet is effective, the target is to have the average systolic blood pressure of this group be below 150. After six months on the diet, an SRS of 28 patients had an average systolic blood pressure of = 143, with standard deviation s = 21. Is this sufficient evidence that the diet is effective in meeting the target? Assume that the distribution of the systolic blood pressure for patients in this group is approximately Normal with mean μ. The P-value for the one-sample t test is: a. between 0.10 and 0.05. b. below 0.01. c. larger than 0.10. d. between 0.01 and 0.05.

d. between 0.01 and 0.05.

A P-value is always computed assuming that the:

null hypothesis is true.

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitudes, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution, with mean of 110 and standard deviation σ = 20. You suspect that incoming freshman have a mean μ, which is different from 110 because they are often excited yet anxious about entering college. To verify your suspicion, you test the hypotheses H0: μ = 110, Ha: μ 110 You give the SSHA to 50 students who are incoming freshman and find their mean score. The P-value of the test of the null hypothesis is the:

probability, assuming the null hypothesis is true, that the test statistic will take a value at least as extreme as that actually observed.

A university administrator obtains a sample of the academic records of past and present scholarship athletes at the university. The administrator reports that no significant difference was found in the mean GPA (grade point average) for male and female scholarship athletes (P = 0.287). This means that:

the chance of obtaining a difference in GPAs between male and female scholarship athletes as large as that observed in the sample if there is no difference in mean GPAs is 0.287.

Suppose the weights of 7th graders at a certain school vary according to a normal distribution with a mean of 100 pounds and a standard deviation of 7.5 pounds. A researcher believes the average weight has decreased since the implementation of a new breakfast and lunch program at the school. For a test of significance, state the null hypothesis. a.μ = 100 This is correct. The null hypothesis is a statement of no effect and gets the equals sign. Text reference: section 17.2 b. μ ≠ 100 c. μ < 100 d. μ > 100

μ = 100