A researcher wants to estimate the average number of days/week UNBC students engage in physical exercises in response to a national fitness magazine article suggesting that the average students in Canada does not engage in physical exercises. She is planning to select a simple random sample of students using the list of currently enrolled students at UNBC after receiving approval from the Research Ethics Board. a. To estimate the average number of days students engage in physical exercises to within 2.5% with a 95% Confidence level, how large should her sample size be if the assumed population standard deviation is 1.5? b. Assuming that based on the above calculated sample size, the researcher observed that the sample average engagement in physical exercise is 2.5 days/week. With a population standard deviation of 1.5, find the 99% confidence interval of this estimate C. What can you say about the 99% Confidence Interval calculated in part b above?

Researchers are investigating whether people who exercise with a training partner have a greater increase, on average, in targeted exercise intensity compared with people who exercise alone. Two methods of collecting data have been proposed. Method I: Recruit volunteers who are willing to participate. Randomly assign each participant to exercise with a training partner or to exercise alone. Method II: Select a random sample of people from all the people who exercise at a community fitness center. Ask each person in the sample whether they use a training partner, and use the response to create the two groups. (a) For each method, the researchers will record the change in targeted exercise intensity for each person in the investigation. They will compare the mean change in intensity between those who exercise with a training partner and those who do not. (i) Describe the population of generalization if method I is used. Explain your answer. (ii) Describe the population of…

An LED light bulb manufacturer claims that the average lifespan of its 60-watt LED light bulbs is 27,000 hours. A corporate watchdog group is suspicious of the company's claim and thinks that the true average lifespan of the 60- watt LED light bulbs produced by the company may be less than the advertised 27,000 hours. The group collected and tested a random sample of 211 light bulbs and found the average lifespan of the sample was 26,941 hours. Use the p-value method to test the hypothesis that the mean lifespan of this brand of 60-watt LED light bulb is less than 27,000 hours, using a = 0.1. Assume the standard deviation of the lifespan of all such light bulbs is known to be 370 hours. State the null and alternative hypothesis for this test. Ho: ? H₁: ? Determine if this test is left-tailed, right-tailed, or two- tailed. right-tailed two-tailed left-tailed Should the standard normal (z) distribution or Student's (t) distribution be used for this test? The Student's t distribution…

The U.S. Energy Information Administration claimed that U.S. residential customers used an average of 10,476 kilowatt hours (kWh) of electricity this year. A local power company believes that residents in their area use more electricity on average than EIA's reported average. To test their claim, the company chooses a random sample of 153 of their customers and calculates that these customers used an average of 10,767 kWh of electricity last year. Assuming that the population standard deviation is 2478 kWh, is there sufficient evidence to support the power company's claim at the 0.05 level of significance? Step 3 of 3: Draw a conclusion and interpret the decision.