# Solved Assignments in Statistics / Hypothesis Testing category

A clinical trial was conducted to test the effectiveness of a drug used for treating insomnia in older subjects. After treatment with the drug, 12 subjects had a mean wake time of 95.6 min and a standard deviation of 42.1 min. Assume that the 12 sample values appear to be from a normally distributed population and construct a 90% confidence interval estimate to the standard deviation of the wake times for a population with the drug treatments. Does the result indicate whether the treatment is effective?
A doctor wants to know if a blood pressure medication is effective. Six subjects have their blood pressures recorded. After twelve weeks on the medication, the same six subjects have their blood pressure recorded again. For this test, only systolic pressure is of concern. Test at the 1% significance level. Patient A B C D E  F Before 161 162 165 162 166 171 After 158 159 166 160 167 169
Two types of phone operating system are being tested to determine if there is a difference in the proportions of system failures (crashes). Fifteen out of a random sample of 150 phones with OS1 had system failures within the first eight hours of operation. Nine out of another random sample of 150 phones with OS2 had system failures within the first eight hours of operation. OS2 is believed to be more stable (have fewer crashes) than OS1. Test appropriate hypothesis.
Two business schools, A and B, located in the same metropolitan area and they are competing for bragging rights. One of the points of competition is average salary of graduating seniors. 30 graduating seniors from A and 25 from B were surveyed. A’s students had an average salary of \$62,000, and B's students had an average salary of \$67,000. Based on historical data, the population standard deviation is assumed to be \$10,000 for A and \$15,000 for B. Construct the hypotheses and conduct the appropriate tests that school B could use to claim that its students have a higher average graduating salary that A. Using a 5% level of significance, and the sample data provided, determine if school B can claim that its average graduating salary is greater than that of school A.
A researcher claims that average body temperature is different for the two genders. A sample of 65 men and 65 women yields average body temperatures of 98.105 and 98.394 oF, respectively. Based on historical data, the standard deviation of body temperature is known to be 0.699 and 0.743 degrees Fahrenheit, respectively. At a 5% level of significance, can you conclude that average body temperature differs with gender? Would your answer change for a 1% level of significance?
The weights of random sample of cereal boxes that are supposed to weight 1 pound are listed here. Estimate $\sigma^2$ of the entire population of cereal of box weights with 95 % confidence. 1.05, 1.03, 0.98, 1.00, 0.99, 0.97, 1.01, 0.96
Researchers at the University of South Florida conducted a study of drug usage of U.S. physicians. The anonymous survey of 5,430 randomly selected physicians revealed that 429 experienced substance abuse or drug dependency in their lifetime. Test the hypothesis that more than 5% of US. physicians have used or depended on drugs in their lifetime at a 0.05. State the null and alternative hypothesis. State your conclusion for your hypothesis test. Give the 95% Confidence Interval. Give a conclusion for the confidence interval test.
A crossover study was conducted to investigate whether oat bran cereal helps to lower serum cholesterol levels in hypercholesterolemic males. Fourteen such individuals were randomly placed on a diet that included either oat bran or corn flakes; after two weeks, their low density lipoprotein (LDL) cholesterol levels were recorded. Each man was then switched to the alternative diet. After a second two week period, the LDL cholesterol level of each individual was again recorded. The data from this study are shown below. Subject LDL (mmol/l) Corn Flakes LDL (mmol/l) Oat Bran 1 4.61 3.84 2 6.42 5.57 3 5.4 5.85 4 4.54 4.8 5 3.98 3.68 6 3.82 2.96 7 5.01 4.41 8 4.34 3.72 9 3.8 3.49 10 4.56 3.84 11 5.35 5.26 12 3.89 3.73 13 2.25 1.84 14 4.24 4.14   a) Are the two samples of data paired or independent?  b) What are the appropriate Null and alternative hypothesis for a two sided test? c) Conduct the test
Suppose that you are interested whether exposure to the organochlorine DDT which has been used extensively as an insecticide for many years, is associated with breast cancer in women. As part of the study that investigated this issue, blood was drawn from a sample of women diagnosed with breast cancer over a six year period and from a sample of healthy controls subject matched to the cancer patients on age, menopausal status, and date of blood donation. Each woman's blood level of DDE-an important by product of DDT in the human body was measured, and the difference in levels for each patient and her matched control calculated. A sample of 171 such differences has mean $\overline{d}=2.7$ ng/ml and standard deviation $s_d =15.9$ ng/ml a) Test the null hypothesis that the mean blood levels of DDE are identical for women with breast cancer and for healthy control subjects. What do you conclude? b) Would you expect a 95% confidence interval for the true difference in population mean DDE lev
A study was conducted to determine whether an expectant mother's cigarette smoking has any effect on the bone mineral content of her otherwise healthy child. A sample of 77 newborns whose mothers smoked during pregnancy has a mean bone mineral content $\overline{x}_1=0.098$ g/cm and standard deviation $s_1=0.026$ g/cm; a sample of 161 infants whose mothers did not smoke has mean $\overline{x}_2= 0.095$ g/cm and standard deviation $s_2=0.025$ g/cm. Assume that the underlying population variances are equal. a) Are the two samples of data paired or independent?  b) State the null and Alternative hypothesis of the two sided test? c) Conduct the test at the 0.05 level of significance. What do you conclude?