Find the test statistic and critical value(s). Also, use the mentioned table to find limits containing the P-value, then determine whether there is sufficient evidence to support the given alternative hypothesis.

Precipitation Amounts $H_1: \sigma \neq 0.25, \alpha=0.01, n=26, s=0.18$.

The TI-83/84 Plus calculator can be used to generate random data from a normally distributed population. The command randNorm(74, 12.5, 100) generates 100 values from a normally distributed population with $\mu=74$ and $\sigma=12.5$ (for pulse rates of women). One such generated sample of 100 values has a mean of $74.4$ and a standard deviation of 11.7. Assume that $\sigma$ is known to be $12.5$ and use a $0.05$ significance level to test the claim that the sample actually does come from a population with a mean equal to 74. Based on the results, does it appear that the calculator's random number generator is working correctly?

Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. OxyContin (oxycodone) is a drug used to treat pain, but it is well known for its addictiveness and danger. In a clinical trial, among subjects treated with OxyContin, 52 developed nausea and 175 did not develop nausea. Among other subjects given placebos, 5 developed nausea and 40 did not develop nausea (based on data from Purdue Pharma L.P.). Use a 0.05 significance level to test for a difference between the rates of nausea for those treated with OxyContin and those given a placebo. Does nausea appear to be an adverse reaction resulting from OxyContin?

Use the data and confidence level to construct a confidence interval estimate of p, then address the given question. The drug OxyContin (oxycodone) is used to treat pain, but it is dangerous because it is addictive and can be lethal. In cljnical trial s, 227 subjects were treated with OxyContin and 52 of them developed nausea (based on data from Purdue Pharma L.P.). Construct a 95% confidence interval estimate of the percentage of OxyContin users who develop nausea.

Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. OxyContin (oxycodone) is a drug used to treat pain, but it is well known for its addictiveness and danger. In a clinical trial, among subjects treated with OxyContin, 52 developed nausea and 175 did not develop nausea. Among other subjects given placebos, 5 developed nausea and 40 did not develop nausea (based on data from Purdue Pharma L.P.). Use a 0.05 significance level to test for a difference between the rates of nausea for those treated with OxyContin and those given a placebo. Use an appropriate confidence interval.

For a study in which subjects are treated with a new drug and then observed, is the study observational or is it an experiment?

Chantix (varenicline) tablets are used as an aid to help people stop smoking. In a clinical trial, 129 subjects were treated with Chantix twice a day for 12 weeks, and 16 subjects experienced abdominal pain (based on data from Pfizer, Inc.). If someone claims that more than 8% of Chantix users experience abdominal pain, that claim is supported with a hypothesis test conducted with a 0.05 significance level. Using 0.18 as an alternative value of p , the power of the test is 0.96. Interpret this value of the power of the test.

In a clinical trial of a drug used to help subjects stop smoking, 821 subjects were treated with 1 mg doses of Chantix. That group consisted of 30 subjects who experienced nausea (based on data from Pfizer, Inc.). The probability of nausea for subjects not receiving the treatment was 0.0124.

b. Based on the result from the previous part, is it unusual to find that among 821 people, there are 30 who experience nausea? Why or why not?

A bottle contains a label stating that it contains Spring Valley pills with 500 mg of vitamin C, and another bottle contains a label stating that it contains Bayer pills with 325 mg of aspirin . When testing claims about the mean contents of the pills, which would have more serious implications: rejection of the Spring Valley vitamin C claim or rejection of the Bayer aspirin claim? Is it wise to use the same significance level for hypothesis tests about the mean amount of vitamin C and the mean amount of aspirin?

An elevator company has redesigned their product to be 50% more energy efficient than hydraulic designs. Two designs are being considered for implementation in a new building. (a) Given an interest rate of 20% which bid should be accepted?

$$\begin{matrix} \text{Alternatives} & \text{A} & \text{B}\\ \text{Installed cost} & \text{\$45,000} & \text{\$54,000}\\ \text{Annual cost} & \text{ 2700} & \text{ 2850}\\ \text{Salvage value} & \text{ 3000} & \text{ 4500}\\ \text{Life, in years} & \text{ 10} & \text{ 15}\\ \end{matrix}$$

(b) Research and list a few attributes that the company might be using in the elevators' major systems drive, cab, hoist, and control mechanisms that make them more energy efficient.

Refer to the histogram provided for the mentioned exercise and construct the frequency distribution that summarizes the outcomes. Then find the mean of the 100 outcomes.

In a Harris poll of 514 human resource professionals, $45.9 \%$ said that body piercings and tattoos were big grooming red flags.

Construct a $99 \%$ confidence interval estimate of the proportion of all human resource professionals believing that body piercings and tattoos are big grooming red flags.

In a Harris poll of 514 human resource professionals, $45.9 \%$ said that body piercings and tattoos were big grooming red flags.

Among the 514 human resource professionals who were surveyed, how many of them said that body piercings and tattoos were big grooming red flags?

Express the confidence interval (0.437,0.529) in the form of $\hat{p} \pm E$.