Problem #04 [10 points 1: A researcher was interested to know whether the American are concerned about the raise of the minimum wage. He randomly selected 200 American and asked if they believed that the minimum wage should be raised. Among 200 respondents 170 said yes. Test the hypothesis that less than 90% of American are concerned about the minimum wage raise. Find the pvalue and make your decision about the null hypothesis at 2% signicance level. Problem #05 (10 points}: The life of a battery in a cardiac pacemaker is assumed to be normally distributed. A life of a battery is subjected to an accelerated life test by running battery continuously at an elevated temperature until failure. A random sample of 40 such tested batteries gave a sample mean of 30.5 hours and standard deviation of 3.5 hours. (a) (7 points) Test the hypothesis that the true mean is more than 29. Use a=0.05. (b) (3 pain ts) Find the power of the test in part (a) when the true mean is 31. Use ct=0.05. Problem #06 [8 points}: A random sample of 36 regions in New England (NE) and a random sample of 34 regions in the Rocky Mountain (RM) states gave the following summary statistics on the violent crimes rate (per milllion people). New Enland Rock Mountain States Do the data indicate that the average violent crime rate in the Rocky Mountain region and the New England are the same? Make your decision about the null hypothesis at a=0.01 level of significance. Which assumptions have you made to validate your test