# Type II errors

Quiz 3

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This quiz has more conceptual questions, because I think they’re important. Be sure to understand the 2×2 box dealing with Type I and Type II errors, alpha, beta, and power.

Each multiple choice questions is worth 0.50 point. Other questions are worth two points.

1. (0.50 point) I hypothesized that girls in my class have the same blood pressure levels as boys. The probability value for my null hypothesis was 0.15. So I conclude that the blood pressures of the girls were higher than boys’. Which kind of mistake did I make?

a. Type I error

b. Type II error

c. Type I and Type II error

d. I did not make any mistake

2. (0.50 point) If a statistical test result is not significant at the 0.05 level, then we can conclude:

a. It is not significant at 0.10 level

b. It must be significant at 0.01 level

c. It must be significant above 0.05 level

d. It is not significant at 0.01 level

3. (2 points) A researcher posed a null hypothesis that there was no significant difference between boys and girls on a standard memory test. She randomly sampled 100 girls and 100 boys in a community and gave them the standard memory test. The mean score for girls was 70 and the standard deviation of mean was 5.0. The mean score for boys was 65 and the standard deviation of mean was 5.0. What is the standard error of the difference in means?

4. (0.50 point) If power is big, you can assume:

a. The significance level set by the researcher must be high

b. We increase the probability of type I error

c. Your study result will be more likely to be inconclusive

d. The difference between the means is more likely to be detected

5. (0.50 point) If the probability that you will correctly reject a false null hypothesis is 0.80 at 0.05 significance level. Therefore, α is__ and β is__.

a. 0.05, 0.80

b. 0.05, 0.20

c. 0.95, 0.20

d. 0.95, 0.80

6. (2 points) The population has a mean of 678 and the population standard deviation is known to be 58.3. Use a 0.05 level of significance to test the claim that the sample scores listed below came from the population. Identify hypotheses, test statistic, P-value or critical value, conclusion about the null, and final conclusion that addresses the original claim.

714 751 664 789 818 779 698 836 753 834 693 802

7. (2 points) I am looking to move to either Mississippi or Arkansas, depending on the cost of housing. Below are the costs (in thousands, hypothetically) of 12 houses in each location based upon a simple random selection:

Mississippi: 155 142 149 130 151 163 151 142 156 133 138 161

Arkansas: 133 140 142 131 134 129 128 140 140 140 137 143

Use a 0.05 significance level to test the claim that the mean cost of houses in Mississippi is greater than the mean cost in Arkansas. Be sure to give the hypotheses, the test statistic with a p-value, and a conclusion.