Math 3339 Section 19377 MWF 10-11am SR 116 (and section 20582 – online) Bekki George [email protected] 639 PGH Office Hours: 11:00 - 11:45am MWF or by appointment Thursday online 5-7 pm EMCF 26 1. A politician wants to know what percentage of the voters support her position on the issue of forced busing for integration. What voter sample should be obtained to determine with 90% confidence the support level to within 4%? a. 21 b. 25 c. 423 d. 601 e. 1691 2. A study was carried out to investigate the effectiveness of a treatment. 1000 subjects participated in the study, with 500 being randomly assigned to the “treatment group” and the other 500 to the “control (or placebo) group”. A statistically significant difference was reported between the responses of the two groups (p-value < .005). Thus, a. there is a large difference between the effects of the treatment and the placebo. b. there is strong evidence that the treatment is very effective. c. there is strong evidence that there is some difference in effect between the treatment and the placebo. d. there is little evidence that the treatment has any effect. e. there is evidence of a strong treatment effect. 3. Suppose we have two SRSs from two distinct populations and the samples are independent. We measure the same variable for both samples. Suppose both populations of the values of these variables are normally distributed but the means and standard deviations are unknown. For purposes of comparing the two means, we use a. Two-sample t procedures b. Matched pairs t procedures c. z procedures d. none of these Section 9.5 - Inferences Concerning Two Population Variances The F – distribution: X 1 / v1 F= X 2 / v2 X 1 , X 2 are chi-squared rv's v1 is the number of numerator degrees of freedom v2 is the number of denominator degrees of freedom Example: Mixed Examples: Do you have an insatiable craving for chocolate or some other food? Since many North Americans apparently do, psychologists are designing scientific studies to examine the phenomenon. According to the New York Times (Feb. 22, 1995), one of the largest studies of food cravings involved a survey of 1000 McMaster University (Canada) students. The survey revealed that 97% of the women in the study acknowledged specific food cravings while only 67% of the men did. Assume that 600 of the respondents were women and 400 were men. Is there sufficient evidence to claim that the true proportion of women who acknowledge having food cravings exceed the corresponding proportion for men? The true average tread lives of two competing brands of radial tires (brand X and brand Y) are known to be normally distributed. The standard deviation of brand X tires is known to be 2200, and the standard deviation of brand Y tires is known to be 1900. A sample of 45 brand X tires results in a sample mean of 42,500 and sample standard deviation of 2450. A sample of 45 brand Y tires results in a sample mean of 40,400 and sample standard deviation of 2150. Find a 95% confidence interval for the difference in the true means, mean of X minus mean of Y. In an experiment to study the effects of illumination level on performance, subjects were timed for completion in both a low light level and high light level. The results are below. Low Light High Light Subject 1 2 3 4 5 26 29 32 26 18 21 23 20 6 7 8 9 21 41 25 25 27 20 25 16 16 25 Can you say with 95% certainty that the average completion time is lower in high light? EMCF 26 4. For a fixed confidence level, when the sample size increases, the length of the confidence interval for a population mean decreases. a. True b. False 5. The z score corresponding to a 98 percent confidence level is 1.96. a. True b. False
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