Researchers conducted trials to investigate the effects of color on creativity. Subjects with a red background were asked to think of creative uses for a brick; other subjects with a blue background were given the same task. Responses were scored. by a panel of judges and results from scores of creativity are given in the accompanying table. Higher scores correspond to more creativity. The researchers make the claim that "blue enhances performance on a creative task." Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b). Click the icon to view the summary statistics. a. Use a 0.05 significance level to test the claim that blue enhances performance on a creative task. What are the null and alternative hypotheses?

Congratulations, you just made a confidence interval! But wait, how did we decide on the width of the interval? The middle of the interval is the sample mean. We start there, and then the "wiggle room" we give on either side of that center is called the margin of error (MOE). There's a formula for margin of error: 0 MOE = 2* √T This formula consists of three values: o is the standard deviation, n is the sample size, and z is a multiplier that we choose based on the confidence level we need. Confidence levels are expressed as percentages, the most common are 90%, 95%, and 99%: * Confidence Z Level value 90% 1.645 95% 1.96 99% 2.576 Let's practice computing a margin of error. For our earlier example about houses, suppose the standard deviation was 14 years, and the sample size was 30. Use a confidence level of 95% and determine the margin of error: σ Remember, we'll use the formula MOE = 2* . First fill in the numbers for each part of the formula: √n = σ= n = Now put it all together,…

Express the confidence interval (0.074, 0.120) in the form of p̂ - E<p<p̂ +E what should replace the question marks? Do not round. ? < p < ?

Express the confidence interval (84.4 %, 95.2 % ) in the form of p ME.

Please help with A and B

Express the confidence intervals (70.3%, 87.9%) in the form of p-hat, plus or minus ME. ? Plus or minus ?

(a) Distinguish between a point estimate and an interval estimate. (b) Why people usually use the term "confidence interval" instead of "probability interval"? Explain your answer carefully.