A study of 420,064 cell phone users found that 136 of them developed cancer of the brain or nervous system. Prior to this study of cell phone​ use, the rate of such cancer was found to be 0.0343​% for those not using cell phones . Use the sample data to construct 95​% confidence interval estimate of the percentage of cell phone users who develop cancer of the brain or nervous system

A sample of 106 body temperatures was taken and the mean was 98.2 degrees F. The population standard deviation is 0.62 degrees.  Use a 0.05 level of significance to test the claim that the average body temperature is actually different than 98.6 degrees F.  Find the 95% confidence interval of the mean temperature and compare your results.

Suppose you work for the Department of Environment and National Resources (DENR). You want to estimate, with 95% confidence, the mean length of all tilapia in a fish hatchery pond. You take a random sample of 10 tilapia and determine the average length is 10.5 inches and the sample standard deviation is 2.9 inches. Construct a confidence interval for this sample and interpret the result.

Is narcissism a more common personality trait today than it was a few decades ago?  It is known that the mean population score on the Narcissistic Personality Inventory (NPI) for students attending University of South Alabama around 20 years ago was μ= 15 (Twenge, 2010).  Interested in the narcissism levels of students in the year 2020, a researcher administers the NPI to a random sample of 25 University of Alabama sophomores this Spring term. The mean NPI score from the researcher’s sample of sophomores is M = 16.5, with s = 3.4. 1. Write the null and alternative hypotheses in symbols. Possible symbols for your answer: H0, H1, μ, M, σ. 2. Calculate the standard error.  3. Find the critical value for the test statistic, assuming alpha = .05 (Use largest [i.e., most conservative] value if exact value not given in the chart)  a) 2.064 b) 1.96 c) 1.98 d) 2.000