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Stat 2000 International – Sample Final - Answers
1. Correct answer: b. H 0 : p = 1/ 2. Correct answer: a. 7. 3. Correct answer: c. The population mean of the population is 0 4. Correct answer: c. A t-interval is a confidence interval estimate of the population mean 5. Correct answer: d. If the population mean is really 12, the probability is 0.006 that the mean of 23 values could be different from 12. 6. Correct answer: b. Sample #2 is large enough to use the z-test. 7. Correct answer: d. The means do not differ 8. Correct answer: d. There are likely to be confounding variables related to both alcohol consumption and depression 9. Correct answer: a. No, there is no linear relationship 10. Correct answer: b. 1. 11. Answers:
a. Ha: Population correlation coefficient 0
b. The probability of a Type I error is 0.05. We do not have enough information to decide what the probability of a Type II error is.
12. Answers:
a. Minitab tells us that the meteorologist's output is "Test of mu = 80.00 vs mu < 80.00." That is, the null hypothesis, H 0 : = 80 , is competing with the alternative hypothesis, Ha: < 80.
b. The question asked: "How likely is it that a sample of 17 people would have an average ideal temperature of 78.6 degrees or less if in fact the population average ideal temperature were 80 degrees? " is the P-value for this hypothesis test. The Minitab output tells us that the calculated P-value is 0.16.
c. The p-value, 0.16, tells us that there is a fair chance of getting a sample average as small as 78.6, if the population average is 80. That is, we shouldn't be surprised at
such a sample average. That is, if we consider a p-value below 0.05 small, then our p-value is not small enough, and therefore we cannot reject the null hypothesis.
d. There is not enough evidence to conclude that the ideal mean temperature for everyone in the population is below 80 degrees Fahrenheit.
13. The alternative hypothesis ( HA ) is that the proportion of the population who can identify the unique beverage is greater than 0.33. 14. Linear Model B, that is, the points are generally farther from the line in model B than model A. 15. Answers: a. Null hypothesis: The proportion of cars with at least 5 defects is constant across days of the week. Alternative hypothesis: The proportion of cars with at least 5 defects is not the same for all days of the week.
b. Null hypothesis: Whether children beginning kindergarten can spell their names is independent of whether or not they attended preschool. Alternative hypothesis: Whether children beginning kindergarten can spell their names depends on whether or not they attended preschool.
36. mean = 6.525, median = 6.5, standard deviation = 0. 37. There are no outliers. But the boxplot indicates that there is some skewness towards the higher values. 38. We have to use a t-statistic (with 15 degrees of freedom) since the population standard deviation is not known and the sample size is relatively small (< 30). The p-value is 0. which is less than 0.05. We reject H0, concluding that the mean milk-pH is clearly different from 6.7. The result is statistically significant. 39. The correlation is -0.9773. This seems to indicate that the points are very close to a line
with negative slope.
48. Sport 1: BMI = 3.78 + 0.5779 * Height Sport 2: BMI = 15.98 + 0.1133 * Height 49. For sport 1, the p-value associated with Height is 0.115 > 0.05,i.e., the slope is not significantly different from 0.For sport 2, the p-value associated with Height is 0.0064 < 0.05, i.e., the slope is significantly different from 0. Just based on our graphical interpretation, we expected the slope for sport 1 to be different from 0 and the slope for sport 2 to be equal to 0. The reason for our graphical misinterpretation is that in the full scatterplot that shows Height versus BMI for both sports, the data for sport 2 appears very condensed at the bottom of the graph, misleading our visual judgement. 50. around 24.
