A team of researchers aims to understand whether a sleep treatment drug has an effect on the number of hours of REM sleep. Five subjects were randomly selected and their time in REM sleep (in minutes) was measured before treatment and after treatment. The before treatment measurements are: (30, 45, 90, 60, 100). The after-treatment measurements for the same five patients are: (35, 30, 80, 70, 110). The researchers compute a 99% confidence interval for the difference (after treatment minus before treatment) in REM sleep time. What is the lower bound of this interval?

In a survey of 2024 adults in a recent​ year, 709 made a New​ Year's resolution to eat healthier.   Construct​ 90% and​ 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence intervals.

Dr. Soria surveyed 34,000+ college students about their rates of housing insecurity during the pandemic. She found that 22% of students experienced housing insecurity (SE = .50). What is the 95% confidence interval for the true proportion of all college students experiencing housing insecurity at that time?

Car and Driver Magazine tested a random sample of 9 hybrid cars and found their MPG to be 42, 51, 39, 44, 52, 48, 51, 44, and 47. Construct a 95% confidence interval for the population variance.

A random sample of high school seniors were asked whether they were applying for college. The resulting confidence interval for the proportion of students applying for college is (0.65,0.69). What is the margin of error?

In a science fair​ project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left​ hand, and then she asked the therapists to identify the selected hand by placing their hand just under​ Emily's hand without seeing it and without touching it. Among 337 trials, the touch therapists were correct 163 times.  Using​ Emily's sample​ results, construct a 95​% confidence interval estimate of the proportion of correct responses made by touch therapists. (round to 3 decimal places)

Wildlife biologists inspect 180 deer taken by hunters and find 36 of them carrying Lyme disease ticks. Calculate a 95% confidence interval for the proportion of deer that carry Lyme disease ticks.

The following table provides the Noradrenaline concentration (µmol/g of creatinine) obtained by analyzing the urine of healthy volunteers between twenty and thirty years of age. Male 0,48 0,36 0,20 0,55 0,45 0,46 0,47 0,23 Female 0,35 0,37 0,27 0,29         Can noradrenaline concentrations be considered to be significantly different between the sexes (considering the 95% confidence level)? Carry out the appropriate hypothesis test, clearly showing how the calculated, critical values (confidence level and degrees of freedom) were obtained and concluding in full whether the null hypothesis is true or not.

To estimate the proportion of students who purchase their textbooks used, 500 students were sampled. 210 of these students purchased used textbooks. Find a 99% confidence interval for the proportion of students who purchase used text books.