Exam 10: Two-Sample Confidence Intervals

The following display from a TI-84 Plus calculator presents a 95% confidence interval for the mean difference between matched pairs. What is the point estimate of $\mu _ { d }$ ?

The following MINITAB output display presents a 95% confidence interval for the difference between two proportions. Sample Sample P 1 116 526 0.220532 2 103 572 0.180070 Difference $= p ( 1 ) - p ( 2 )$ Estimate for difference: $0.040462$ $95 \%$ CI for difference: $( - 0.014,0.095 )$ Fill in the blanks: We are 95% confident that the difference between the proportions is between ______ and ______.

A group of six individuals with high blood pressure volunteered to test whether petting cats for 10 minutes can alter systolic blood pressure levels. Systolic blood pressures (in millimeters of mercury, Or mmHg) were measured for each subject before and after petting cats for 10 minutes, with the Following results: Individual Before After 1 149 177 2 175 214 3 194 189 4 186 150 5 180 171 6 164 168 Find the 99% confidence interval for the mean reduction in systolic blood pressure.

Traffic engineers compared rates of traffic collisions at intersections with raised medians and rates at intersections with two-way left-turn lanes. They found that out of 4,512 collisions at intersections With raised medians, 2,202 were rear-end collisions, and out of 4,277 collisions at two-way left-turn Lanes, 1,903 were rear-end collisions. Assuming these to be random samples of collisions from the two types of intersections, construct a 95% Confidence interval for the difference between the proportions of collisions that are of the rear-end Type at the two types of intersection. Does the confidence interval contradict the claim that the Proportion of rear-end collisions is the same at both types of intersection?

In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Fourteen randomly selected plots of land were treated with fertilizer A, and 10 randomly Selected plots were treated with fertilizer B. The number of pounds of harvested fruit was measured From each plot. Following are the results. Assume that the populations are approximately normal. Construct a 95% confidence interval for the Difference between the mean yields for the two types of fertilizer.

The following display from a TI-84 Plus calculator presents a 95% confidence interval for the difference between two proportions. Fill in the blanks: We are 95% confident that the difference between two proportions is between _______ and _______.

The following output from MINITAB presents a confidence interval for the mean difference between matched pairs. Mean StDev SEMean Difference 14 3.2680 7.2315 1.9327 95\% CI for mean difference: (-0.907337,7.443337) How many degrees of freedom are there?

A group of six individuals with high blood pressure volunteered to test whether petting cats for 10 minutes can alter systolic blood pressure levels. Systolic blood pressures (in millimeters of mercury, Or mmHg) were measured for each subject before and after petting cats for 10 minutes, with the Following results: Individual Before After 1 178 156 2 200 157 3 217 183 4 192 170 5 177 172 6 193 175 A researcher claims that the mean reduction in systolic blood pressure is 14 mmHg. Does the 98% Confidence interval contradict this claim? (Hint: you need to find the 98% confidence interval for The mean reduction in systolic blood pressure.)

A survey of college students reported that in a sample of 442 male students, the average number of energy drinks consumed per month was 1.82 with a standard deviation of 4.84, and in a sample of 80 female students, the average was 1.89 with a standard deviation of 3.26. Construct a 98% confidence interval for the difference between men and women in the mean number Of energy drinks consumed. Based on your results, is it reasonable to believe that the mean number Of energy drinks consumed may be the same for both male and female students?

Using technology, solve the following problem: In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Fourteen randomly selected plots of land Were treated with fertilizer A, and 10 randomly selected plots were treated with fertilizer B. The Number of pounds of harvested fruit was measured from each plot. Following are the results. Assume that the populations are approximately normal. Construct a 98% confidence interval for the Difference between the mean yields for the two types of fertilizer.

A sample of students is enrolled in a speed-reading class. Each takes a reading test before and after the class. The two samples of scores are compared to determine how large an improvement in Reading speed occurred. Are these samples independent or paired?

An amateur golfer wishes to determine if there is a difference between the drive distances of her two favorite drivers. (A driver is a specialized club for driving the golf ball down range.) She hits fourteen balls With driver A and 10 balls with driver B. The drive distances (in yards) for the trials are show below. Assume that the populations are approximately normal. Construct a 90% confidence interval for the Difference between the mean drive distances for the two drivers.

The following MINITAB output display presents a 95% confidence interval for the difference between two means. Mean StDev SE Mean 13 111.071 22.131 6.138 15 97.224 26.446 6.828 How many degrees of freedom did MINITAB use?

The following display from a TI-84 Plus calculator presents a 95% confidence interval for the difference between two proportions. Compute the point estimate of $p _ { 1 } - p _ { 2 }$

The following display from a TI-84 Plus calculator presents a 95% confidence interval for the mean difference between matched pairs. How many degrees of freedom are there?

Construct the confidence interval for the difference $p _ { 1 } - p _ { 2 }$ for the given level and values of $x _ { 1 } , n _ { 1 }$ , $x _ { 2 }$ , and $n _ { 2 }$ . Level $98 \% : x _ { 1 } = 27 , n _ { 1 } = 64 , x _ { 2 } = 16 , n _ { 2 } = 55$

In a random sample of 70 patients undergoing a standard surgical procedure, 16 required medication for postoperative pain. In a random sample of 85 patients undergoing a new procedure, only 17 Required medication. Construct a 98% confidence interval for the difference in the proportions of patients needing pain Medication between the old and new procedures. A physician claims that the proportion of patients Who need pain medication is the same for both procedures. Does the confidence interval contradict The claim?

The following display from a TI-84 Plus calculator presents a 95% confidence interval for the mean difference between matched pairs. Fill in the blanks: We are 95% confident that the mean difference is between ______ and ______.

The following output from MINITAB presents a confidence interval for the mean difference between matched pairs. \begin{array} { r r r r r } & \mathrm { N } & \text { Mean } & \text { StDev } & \text { SEMean } \\ \text { Difference } & 15 & 6.0341 & 2.8059 & 0.724738 \end{array}\\ $95 \%$ CI for mean difference: $( 4.4797,7.5885 )$ Fill in the blanks: We are $95 \%$ confident that the mean difference is between____ and_____

The following MINITAB output display presents a 95% confidence interval for the difference between two means. Mean StDev SE Mean A 15 144.384 25.413 6.562 B 9 168.966 22.669 7.556 Difference = mu (A) - mu (B) Estimate for difference: -24.582 95\% CI for difference: (-44.197,-4.967) DF =19 Fill in the blanks: We are 95% confident that the difference in the means is between ______ And ______.