Problem 6. A pharmaceutical company is evaluating the effectiveness of a new drugto treat insomnia. For a random group of 64 patients the average amount of sleep is 5hours per night before receiving the drug. After one month of treatment, the averageamount of sleep is 5.8 hours per night. The standard deviation of the differences is 0.6.Can the new drug be considered effective?a. Setup the appropriate null and alternative hypotheses.b. Construct the relevant test statistic.c. Test the hypotheses at the 0.05 significance level and state your conclusion.

Answered: Problem 6. A pharmaceutical company is…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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-stating correctly whether the test is a one-tailed or two-tailed test - stating the correct Null and Alternative Hypotheses. -stating the alpha (z-value from unit normal table) for the boundary of the critical region for a one-tailed test or two-tailed test. -calculating OM -calculating the test statistic (z-score)
The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.8 auto accidents per day with a standard deviation of 0.04. The actuaries of the company claim that the standard deviation of the number of accidents per day is no longer equal to 0.04. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H, and the alternative hypothesis H,1 that we would use for this test. Ho H: 0 O
2) A restaurant association claims that the average amount a family spends per year eating out is $2700. Suppose you are a consumer reporter and want to test this claim. You select a random sample of 32 homes and obtain that their mean is $2850 with a standard deviation of $270. using α= 0.05, do you have enough evidence to reject the association's claim?
Under what circumstances is a t statistic used instead of a z-score for a hypothesis test? Justin wants to know whether a commonly prescribed drug does improve the attention span of students with attention deficit disorder (ADD). He knows that the mean attention span for students with ADD who are not taking the drug is 2.3 minutes long. His sample of 12 students taking the drug yielded a mean of 4.6 minutes. Justin can find no information regarding σx , so he calculated s2x =1.96. Determine the critical region using a one-tailed test with alpha = .05. Conduct the hypothesis test (Do the math and compare the t-critical and t-obtained values). State your conclusions in terms of H0 (Should you reject the H0 or fail to reject/accept the H0). Based on your analysis, is there a relationship between the drug and attention span?
Is the following statements correct or incorrect: Suppose that a random vector Y' = (Y1, Y2, Y3) has multi-normal distribution with mean vector u and variance-covariance matrix £ given by and Σ 흑 0 1 respectively. CH), Then the distribution of Z = Y is N 1
Question 3 Assume the average teenager sends 250 text messages per day. You sample 28 local teenagers and find that they send 232 messages per day with a standard deviation (calculated with the correction) of 64 messages per day. What decision would you make based on these data? Fail to reject the null hypothesis; we cannot conclude that there is any difference between our sample and the nation. Fail to reject the null hypothesis; the local teenagers text more than the national average. Reject the null hypothesis; there is no evidence of a difference between our sample and the nation. Reject the null hypothesis; our sample sends significantly fewer text messages than the national average.
Hunter is writing a report on the backgrounds of American presidents. He finds that the mean age of the 45 presidents is 55 years with the standard deviation of 6.59 years. Because Hunter took a statistics course, he calculates a 95% confidence interval for the mean age of all men who have been president to be 55 ± 1.98. Comment on this result. Question 8 options: Hunter can be 95% confident that the mean age of all presidents is 55 years. 95% of all the ages of the presidents lie between 55 ± 1.98. Hunter should have taken a larger sample to reduce the margin of error. Hunter is 95% confident that the mean age of all presidents lies between 53.02 and 56.98 years. The confidence interval makes no sense since Hunter has the entire population of ages.
1. In a random sample of fishes from a pond, the mean tail length was 6.0 mm and the reference tail length for the species was found to be 4.0 mm with a standard deviation of 2.0. if there are 16 fishes, what would be the z score and which hypothesis would be accepted? 2. If the mean for group 1 in a clinical trial for the time for a drug X to act is 10 minutes and 8 minutes for group 2 and if the standard deviation for group 1 is 1.0 and group 2 is 2.0. If there are 4 persons in both groups, what is the t value and which hypothesis would you accept if t critical is 3.14 ( 2 sided) 3. A geneticist is examining the relationship between genotype and phenotype for roses. He calculated a chi-square value of 4.1 for a 2 x 2 table. If the scenario is two sided, which hypothesis did he accept? 4.
Solve question #9 for part D only.
Your restaurant believes that the average bill for a party of four exceeds $100. To test this a random sample of 25 parties is selected. The average bill comes to $108 with a variance of $225. a. Set up hypotheses to see if the average bill exceeds $100. b. Report your result along with the p value or alpha (Type I error) level of your choosing. c. Offer your conclusions.
The records of a casualty insurance company show that, in the past, its clients have had a mean of 1.9 auto accidents per day with a standard deviation of 0.04 . The actuaries of the company claim that the standard deviation of the number of accidents per day is no longer equal to 0.04. Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis H0 and the alternative hypothesis H1 that we would use for this test. H0 : __? H1 : __?

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