Stat 200 quiz 8

B Feedback: The p-value is found on the presumption that the null hypothesis is true, not the alternative.

Which of the following is not one of the steps for hypothesis testing? A) Verify data conditions and calculate a test statistic. B) Assuming the alternative hypothesis is true, find the p-value. C) Determine the null and alternative hypotheses. D) Assuming the null hypothesis is true, find the p-value.

F Feedback: The word not is the key term in determining the correct Ha expression. Not implies that the investigator is interested in whether the true population mean is not equal to 21. The value of 22.2 is the sample mean.

A counselor wants to show that for men who are married by the time they are 30, μ = average age when the men are married is not 21 years old. A random sample of 10 men who were married by age 30 showed an average age at marriage of 22.2, with a sample standard deviation of 1.9 years. Assume that the age at which this population of men gets married for the first time is normally distributed. What are the appropriate null and alternative hypotheses? A) Ho: μ = 21 and Ha: μ >21 B) Ho: μ = 21 and Ha: μ < 21 C) Ho: μ ≠ 21 and Ha: μ = 21 D) Ho: x-bar ≠ 21 and Ha: x-bar = 21 E) Ho: x-bar = 21 and Ha: x-bar ≠ 21 F) Ho: μ = 21 and Ha: μ ≠ 21 G) Ho: x-bar = 21 and Ha: x-bar < 21 H) Ho: x-bar = 21 and Ha: x-bar > 21

C Feedback: The z-statistic is found by (ρ-hat - ρ)/√[(ρ*(1-ρ))/n]

A hypothesis test for a population proportion ρ is given below: Ho: ρ = 0.10 Ha: ρ ≠ 0.10 If the sample size n = 500 and sample proportion ρ-hat = 0.20, then the z-statistic is: A) 5.59 B) -7.45 C) 7.45 D) -5.59

C Feedback: Since Ha is ">" we find the p-value by P(Z > z) where z is the z-statistic.

A hypothesis test for a population proportion ρ is given below: Ho: ρ = 0.40 Ha: ρ > 0.40 Use Standard Normal Table to calculate the p-value for this hypothesis test for z-statistic = 0.00 the p-value is: A) 0.3085 B) 0.0000 C) 0.5000 D) 0.6915

C Feedback: Since Ha is ">" we find the p-value by P(Z > z) where z is the z-statistic.

A hypothesis test for a population proportion ρ is given below: Ho: ρ = 0.40 Ha: ρ > 0.40 Use Standard Normal Table to calculate the p-value for this hypothesis test for z-statistic = 2.00 the p-value is: A) 0.9332 B) 0.9545 C) 0.0228 D) 0.9772

D Feedback: Since Ha is "≠" we find the p-value by twice the P(Z > |z|) where z is the z-statistic.

A hypothesis test for a population proportion ρ is given below: Ho: ρ = 0.70 Ha: ρ ≠ 0.70 Use Standard Normal Table to calculate the p-value for this hypothesis test for z-statistic = -1.00 the p-value is: A) 0.1587 B) 0.6348 C) 0.8413 D) 0.3174

B Feedback: Since the p-value is > 0.05 we would not reject Ho. Therefore, the result does not provided statistically significant evidence against the null hypothesis that ρ = 0.5

A researcher examined the folklore that women can predict the sex of their unborn child better than chance would suggest. She asked 104 pregnant women to predict the sex of their unborn child, and 57 guessed correctly. Using these data, the researcher created the above Minitab output. Based on the information in the output and using α = 0.05, what is the appropriate conclusion the researcher can make about ρ = proportion of pregnant women who can correctly predict the sex of their unborn child? A) There is statistically significantly evidence against the null hypothesis that p = 0.5. B) There is not statistically significant evidence against the null hypothesis that p = 0.5. C) There is not statistically significant evidence against the null hypothesis that p = 0.548. D) There is statistically significant evidence against the null hypothesis that p = 0.548.

D Feedback: The word less is the key term in determining the correct Ha expression. Less than implies that the investigator is only interested in whether the true population mean is less than 25. The value of 24 is the sample mean. The test statistic, t is found by taking the difference between the sample mean (24) minus the hypothesized mean (25) and dividing by the standard error of the mean (S/√n = 2.2/√14 = 0.588). The t-value is then t = −1/0.588 = −1.70. Then with degrees of freedom of 14 − 1 = 13 and from T-table we get 0.05 < p-value < 0.10 and since this range exceeds 0.05 we say "No, results are not statistically significant".

A safety officer wants to prove that μ = the average speed of cars driven by a school is less than 25 mph. Suppose that a random sample of 14 cars shows an average speed of 24.0 mph, with a sample standard deviation of 2.2 mph. Assume that the speeds of cars are normally distributed. Using the T-table, for a significance level of a = 0.05, are the results statistically significant? A) Yes, results are statistically significant because the p-value range does NOT exceed 0.05 B) Yes, results are statistically significant because the p-value range exceeds< 0.05. C) No, results are not statistically significant because the p-value range does NOT exceed 0.05 D) No, results are not statistically significant because the p-value range exceeds 0.05.

B Feedback: This is a one sample t-test, so the test statistic, t is found by taking the difference between the sample mean (24) minus the hypothesized mean (25) and dividing by the standard error of the mean (S/√n = 2.2/√14 = 0.588). The t-value is then t = −1/0.588 = −1.70.

A safety officer wants to prove that μ = the average speed of cars driven by a school is less than 25 mph. Suppose that a random sample of 14 cars shows an average speed of 24.0 mph, with a sample standard deviation of 2.2 mph. Assume that the speeds of cars are normally distributed. What is the value of the test statistic? A) t = −1.80 B) t = −1.70 C) t = −1.50

B Feedback: Changing Ha from a one-sided test (i.e. > or <) to a two-sided test (i.e. ≠) the p-value would double. Conversely, if we altered the test from a 2-sided to a 1-sided test the p-value would be cut by half.

A sample of n = 200 college students is asked if they believe in extraterrestrial life and 120 of these students say that they do. The data are used to test Ho: ρ = 0.5 versus Ha: ρ > 0.5, where p is the population proportion of college students who say they believe in extraterrestrial life. From this sample, the above Minitab output was obtained. Suppose that the alternative hypothesis had been Ha: ρ ≠ 0.5. What would have been the p-value of the test? A) 0.5 B) 0.004 C) 0.002 D) 0.001

D Feedback: With Ha: ρ > 0.5 and having rejected Ho since p-value is less than 0.05, we would conclude that the proportion of college students who say they believe in extraterrestrial life seems to be greater than 50%.

A sample of n = 200 college students is asked if they believe in extraterrestrial life and 120 of these students say that they do. The data are used to test Ho: ρ = 0.5 versus Ha: ρ > 0.5, where p is the population proportion of college students who say they believe in extraterrestrial life. From this sample, the above Minitab output was obtained. Using a 5% significance level, what is the correct conclusion for this significance test? A) The proportion of college students who say they believe in extraterrestrial life is not equal to 50%. B) The proportion of college students who say they believe in extraterrestrial life seems to be equal to 60%. C) The proportion of college students who say they believe in extraterrestrial life is equal to 50%. D) The proportion of college students who say they believe in extraterrestrial life seems to be greater than 50%.

B Feedback: With Ha: ρ > 0.5 and having rejected Ho since p-value is less than 0.05, we would conclude that the proportion of college students who say they believe in extraterrestrial life seems to be greater than 50%.

A sample of n = 200 college students is asked if they believe in extraterrestrial life and 120 of these students say that they do. The data are used to test Ho: ρ = 0.5 versus Ha: ρ > 0.5, where p is the population proportion of college students who say they believe in extraterrestrial life. From this sample, the above Minitab output was obtained. Using a 5% significance level, what is the correct conclusion for this significance test? A) The proportion of college students who say they believe in extraterrestrial life seems to be equal to 60%. B) The proportion of college students who say they believe in extraterrestrial life seems to be greater than 50%. C) The proportion of college students who say they believe in extraterrestrial life is equal to 50%. D) The proportion of college students who say they believe in extraterrestrial life is not equal to 50%.

A Feedback: With a p-value of 0.002 which is less than 0.05 we would reject the null hypothesis.

A sample of n = 200 college students is asked if they believe in extraterrestrial life and 120 of these students say that they do. The data are used to test Ho: ρ = 0.5 versus Ha: ρ > 0.5, where p is the population proportion of college students who say they believe in extraterrestrial life. From this sample, the above Minitab output was obtained. Using a 5% significance level, what is the correct decision for this significance test? A) Reject the null hypothesis because the p-value is less than 0.05. B) Reject the null hypothesis because the p-value is greater than 0.05. C) Fail to reject the null hypothesis because the p-value is greater than 0.05. D) Fail to reject the null hypothesis because the p-value is less than 0.05.

D Feedback: The p-value means the observed data would not be very likely to occur if we believe the null hypothesis is true. So we believe in our data and disbelieve the null hypothesis.

About 90% of the general population is right-handed. A researcher speculates that artists are less likely to be right-handed than the general population. In a random sample of 100 artists, 83 are right-handed. Which of the following best describes the p-value for this situation? A) The probability that the population proportion of artists who are right-handed is 0.90. B) The probability that the population proportion of artists who are right-handed is less than 0.90, given that the sample proportion is 0.83. C) The probability that the population proportion of artists who are right-handed is 0.83. D) The probability the sample proportion would be as small as 0.83, or even smaller, if the population proportion of artists who are right-handed is actually 0.90.

A Feedback: As with confidence intervals, hypothesis statements are statements made toward the population, thus use population parameters

Null and alternative hypotheses are statements about A) population parameters. B) sample parameters. C) it depends - sometimes population parameters and sometimes sample statistics. D) sample statistics.

A Feedback: With p-value <e; α our decision is to reject the null hypothesis Ho

Suppose the significance level for a hypothesis test is α = 0.05. If the p-value is 0.001, the decision is to A) reject the null hypothesis. B) not reject the null hypothesis. C) accept the null hypothesis.

B Feedback: With p-value <e; α our decision is to reject the null hypothesis Ho

Suppose the significance level for a hypothesis test is α = 0.05. If the p-value is 0.049, the decision is to A) not reject the null hypothesis. B) reject the null hypothesis. C) accept the null hypothesis.

A Feedback: The test statistic (z for proportions and t for means) is what is used to calculate the p-value

The data summary used to calculate the p-value in order to decide between the null hypothesis and the alternative hypothesis is called a A) test statistic. B) p-value. C) significance level. D) statistically significant result.

C Feedback: When we go from a 1-sided test of hypotheses to a 2-sided test we would double the p-value. Conversely, going from a 2-sided to a 1-sided we would cut the p-value in half.

The p-value for a one-sided test for a mean was 0.04. The p-value for the corresponding two-sided test would be: A) 0.06 B) 0.02 C) 0.08 D) 0.04

C Feedback: Hypothesis tests are NOT about the sample, but instead we use the sample to draw conclusions about the population.

Which statement is not true about hypothesis tests? A) Hypothesis tests are only valid when the sample is representative of the population for the question of interest. B) Conclusions are statements about the population represented by the samples. C) Hypotheses are statements about the sample (or samples) from the population. D) Hypotheses are statements about the population represented by the samples.