1. A researcher collected a sample of data regarding the mean number of hours a person spends online performing work tasks during the current COVID-19 pandemic. A 95 % confidence level

is computed with appears to be very broad. Explain what things the researcher could do to make the confidence interval narrower.

2. A pharmaceutical company scientist is testing whether the mean level of a toxin in a newly created children's medicine is less than 5mg, a level which could damage the children taking it.

a. If the test were conducted on a sample of 5,000 bottles, explain how the results could give significant results, but still make the company hesitant about making the medicine.

b. 5% is a very common significance level for significance tests, but it Is arbitrary. In this case, explain what you might change the significance level to and why you would consider changing it.

3. A market researcher chooses at random from people entering a large upscale department store. One outcome of the study is a 95% confidence interval for the mean of "the highest price you would pay for a handbag". Explain why this confidence interval does not give useful information about the population of all people also explain what information the 95% confidence interval does provide.

4. A recent survey collected a sample of size n in which it asked nurses about their yearly salary. The average yearly salary was determined to be $67,250, and the population standard deviation is known to be $7,804. You want to create a 90% confidence interval with this information, how large must your sample size n be such that your margin of error is $1,500?

5. A double-blind randomized experiment compared the effects of the drug Lorcaserin and placebo on weight loss in overweight adults. All subjects were also required to undergo diet and exercise counseling. The study involved 1000 participants where half of them would take

Lorcaserin and half the placebo. The researchers found that after a year the treatment group had an average weight loss of 5.8 kg while the placebo group had an average weight loss of 3.9 kg. Based on this information researchers need to decide if Locarserin can be a possible treatment for weight loss.

a. What would be a Type I error in this context? Your answer should consist of both the researchers' decision and what the reality is.

b. What would be a Type II error in this context? Your answer should consist of both the researchers' decision and what the reality is.