Exercises on Confidence Intervals and Hypothesis Testing1. A

Exercises on Confidence Intervals and Hypothesis Testing1. A random sample of 225people was drawn from the total population of Washington, DC. Their average agewas 32.4 years, and the sample standard deviation was 11.8 years. a) Calculate a 95% confidenceinterval for the population mean. b) Interpret the meaning of theconfidence interval you calculated in one sentence. 2. A random sample of 144students was drawn from the population of all students at CUA. Each student wasgiven an IQ test. The average score was 104, with a sample standard deviationof 15. Perform a test of the hypothesis that the true population mean is 100,using a significance level of 5% (alpha = 0.05). a) What are the null andalternative hypotheses? b) Draw a picture of thestandard normal distribution, labeling the mean, the z-score, the criticalvalues, and the rejection regions. Show your work for calculating the z-score. c) What is the result of yourhypothesis test? 3. A random sample of 144 studentswas drawn from the population of all students at CUA. Each student was given anIQ test. The average score was 102, with a sample standard deviation of 15.Perform a test of the hypothesis that the true population mean is 100, using asignificance level of 1% (alpha = 0.01). a) What are the null andalternative hypotheses? b) Draw a picture of thestandard normal distribution, labeling the mean, the z-score, the criticalvalues, and the rejection regions. Show your work for calculating the z-score. c) What is the result of yourhypothesis test? 4.Consider the same sample and test results that were used in question 3. Performa test of the hypothesis that the true population mean is 100 against thealternative hypothesis that the true population mean is greater than 100. Use asignificance level of 5% (alpha = 0.05). a) What are the null andalternative hypotheses? b) Draw a picture of thestandard normal distribution, labeling the mean, the z-score, the criticalvalues, and the rejection regions. Show your work for calculating the z-score. c) What is the result of yourhypothesis test? 5. A random sample of 25students was drawn from the population of all students at CUA. Each student wasgiven an IQ test. The average score was 102, with a sample standard deviationof 15. Perform a test of the hypothesis that the true population mean is 100,using a significance level of 10% (alpha = 0.1). a) What are the null andalternative hypotheses? b) Calculate the t-score,showing your work. What are the critical values? c)What is the result of your hypothesis test?