In random, independent samples of 400 adults and 275 teenagers who watched a certain television show, 224 adults and 121 teens indicated that they liked the show. Let p₁ be the proportion of all adults watching the show who liked it, and let p₂ be the proportion of all teens watching the show who liked it. Find a 95% confidence interval for p₁-P₂. Then find the lower limit and upper limit of the 95% confidence interval. Carry your intermediate computations to at least three decimal places. Round your responses to at least three decimal places. (If necessary, consult a list of formulas.) Lower limit: X Upper limit: 1

A retrospective study of 100 pairs of twins was performed. The twin pairs each had one male child and one female child. Their birth weights were studied to determine if the male twin was consistently heavier.  The difference in weights was calculated by subtracting the female weight (in ounces) from the male weight (in ounces):  d=xm−xfd=xm-xf  After looking at 100 pairs of twins, the study finds the 95% confidence interval for the mean difference of weights (in ounces) is: 1.9 < μdμd < 6.7 Can we be reasonably sure that the male twins are heavier than the females?   Yes No   Why or why not?

A random sample of 500 patients with diabetes were weighed before and after switching to a new drug and the change in their weight is computed for each patient. The resulting 90% confidence interval for the average change in the weight of diabetes patients is (1, 5) expressed in pounds. Which of the following can be the 95% confidence interval generated from the same data?

One company recently conducted a survey in which 420 women and 420 men were asked "Are you satisfied with the work of the Minister of Health?". Of these, 155 men and 118 women said they were satisfied with the minister's work. Assume that the experimental design was correct. Questions 1 and 2 cover this survey. 1. Find the upper limit of 95% confidence interval for the difference in the proportion of men and women who are happy with the work of the Minister (let men be group 1). 1. 0.03. 2. 0.09. 3. 0.15. 4. It is not possible to apply a normal approach and therefore we can not calculate the confidence interval. 2. What is the rejection area if it is to be examined whether the proportion of men and women who are satisfied with the job of Prime Minister is different (use a = 0.05)? 1. RejectHO efz 1.96. 2. Reject HO if z> 1.64. 3. RejectHO efz> -1.96 or <1.96. 4. Insufficient information provided to answer this.

In random, independent samples of 200 adults and 300 teenagers who watched a certain television show, 124 adults and 153 teens indicated that they liked the show. Let p, be the proportion of all adults watching the show who liked it, and let p, be the proportion of all teens watching the show who liked it. Find a 90% confidence interval for p,-p,. Then find the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three decimal places. Round your responses to at least three decimal places. (If necessary, consult a list of formulas.) Lower limit: Upper limit: O O

Two different researchers measured the weight of two separate samples of ruby-throated hummingbirds from the same population. Each calculated a 95% confidence interval for the mean weight of these birds. Researcher 1 found the 95% confidence interval to be 3.12 g < μ < 3.48 g while Researcher 2 found the 95% confidence interval to be 3.05g < μ < 3.62 g.   Why would the two researchers get different answers? Which researcher most likely had the larger sample? Can you be certain about your answer in part (b)? Why or why not?