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1.)For students who first enrolled in two year public institutions in a recent semester, the proportion who earned a bachelor’s degree within six years was 0.3950.395.The president of a certain college believes that the proportion of students who enroll in her institution have a lowerlower completion rate.(a)Determine the null and alternative hypotheses.(b)Explain what it would mean to make a Type I error.(c)Explain what it would mean to make a Type II error.2.)A simple random sample of size n = 17is drawn from a population that is normally distributed. The sample mean is found to be x overbar =70 and the sample standard deviation is found to be s =15. Construct a 90% confidence interval about the population mean. The 90% confidence interval is ??3.) In a random sample of 38 criminals convicted of a certain crime, it was determined that the mean length of sentencing was 59 months, with a standard deviation of 9 months. Construct and interpret a 95% confidence interval for the mean length of sentencing for this crime.Select the correct choice below and fill in the answer boxes to complete your choice.(Use ascending order. Round to one decimal place as needed.)A. 95% of the sentences for the crime are between and months.B. There is a 95% probability that the mean length of sentencing for the crime is betweenand months.C. We can be 95% confident that the mean length of sentencing for the crime is between and months.4.) A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x overbarx, is found to be114, and the sample standard deviation, s, is found to be 10.(a) Construct a 90% confidence interval about μ if the sample size, n, is 11.(b) Construct a 90% confidence interval about μ if the sample size, n, is 16.(c) Construct a 96%confidence interval about μ if the sample size, n, is 11.(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
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