A clinical trial was planned to compare the effect of a new active treatment with that of the standard treatment. Before they started the trial, the 11 subjects who were to receive the new treatment had scores with a sample standard deviation of 6.9, whereas the 9 subjects who were to receive the standard treatment had scores with a sample standard deviation of 5.2. (a) Carry out an appropriate hypothesis test to determine whether the populations from which the two samples are drawn have the same variance. State all the details for your hypothesis test clearly. (b) State clearly the assumptions you need for your test to be valid. (c) Calculate a 95% confidence interval for the ratio of the variances, stating clearly the ratio you are using.

A year-long fitness centre study sought to determine if there is a relationship between the amount of muscle mass gained (kilograms) and the weekly time spent working out under the guidance of a trainer (minutes). They take a simple random sample of 100 subjects in the centre. Based on the sample, they observe that the muscle mass gain variable has mean 15.65 kg and standard deviation 2.1 kg. In addition, they also observe the variable of weekly time spent on working out has mean 114 minutes with standard deviation 13 minutes. From the scatter plot, they find that the correlation between these two variables is 0.83. a. Find the response variable and explanatory variable in this study? b. Using the sample information, find the slope of the least square regression line? Interpret the slope of the regression. c. Using the sample information, find the intercept of the least square regression line? Interpret the intercept of the regression. d. From part b and c, determine the regression…

Research has shown that, for baseball players, good hip range of motion results in improved performance and decreased body stress. A research article reported on a study of independent samples of 40 professional pitchers and 40 professional position players. For the pitchers, the sample mean hip range of motion was 75.5 degrees and the sample standard deviation was 5.8 degrees, whereas the sample mean and sample standard deviation for position players were 79.1 degrees and 7.1 degrees, respectively. Assuming that the two samples are representative of professional baseball pitchers and position players, test hypotheses appropriate for determining if there is convincing evidence that the mean range of motion for pitchers is less than the mean for position players. (Use  ? = 0.05.  Use ?1 for pitchers and ?2 for position players.) State the appropriate null and alternative hypotheses.   Find the test statistic and P-value. (Use SALT. Round your test statistic to one decimal place and…

A clinical trial for a psychological therapy for trauma takes 37 women and gives them one treatment for trauma and then, a year later, gives them a different treatment. The measure used to indicate success is a Likert scale where 5 means 'l found the treatment very helpful' and 1 means 'l didn't find it helpful at all. The lead researcher gathers the data and she finds a very high variance of scores across the women in each treatment, and considers giving up the analysis. She plans to do a difference in means analysis with unequal variances (she tested and found the variances were unequal). She asks for your advice:   a. She is being too hasty because she is using the wrong technique. This is a paired sample and when she takes the difference in the Likert scale for each subject across the two treatments the variance of the remaining lifferences might be so low that she can detect which treatment is statistically better b. She cannot give different treatments to the same people - it…

Over the years, a sushi restaurant has had a mean customer satisfaction rating of 72.5 with a variance of 24.7. The owner has hired you to perform a hypothesis test to see if using a new menu will have any effect on the variance, o“. To do so, you survey a random sample of 19 customers who ordered from the new menu. For the customers surveyed, the variance of ratings is 44.3. Under the assumption that the customer ratings using the new menu follow a normal distribution, you will perform a chi-square test. Find x, the value of the test statistic for your chi-square test. Round your answer to three or more decimal places.

Scientists are working on a synthetic vaccine (antigen) for the parasitic roundworm. The success of the vaccine hinges on the characteristics of DNA in peptide (protein) produced by the antigen. In the journal, Gene Therapy and Molecular Biology (June, 2009), scientists tested alleles of antigen-produced protein for level of peptide. For a sample of 24 alleles, the mean peptide score was 1.83 and the standard deviation was .15. Use this information to construct a 95% confidence interval for the true mean peptide score in alleles of the antigen-produced protein.

Two soap brands have a competition over the longevity of their bars. A sample of 21 bars from company A lasts an average of 13.1 days with a sample variance of 21.2. A sample of 24 bars from company B lasts for an average 10.3 days with a sample variance of 19.3. Test to see if company A’s variance is larger than company B's variance using a 5% level of significance. The null hypothesis is that the variances are the same. The alternate hypothesis is that company A’s variance is larger than company B’s variance. Report your conclusion: a) fail to reject the null hypothesis b) reject the null hypothesis

An educational psychologist is studying two methods of tutoring young children: Method A and Method B. She wants to test whether there is any difference in puzzle solving skills between children tutored by one method versus children tutored by the other. Independent samples of 15 children who were tutored using Method A and 9 children who were tutored using Method B were chosen at random. The Method A children took a mean of 35 minutes to solve a certain puzzle with a standard deviation of 6 minutes. The Method B children took a mean of 44 minutes to solve the same puzzle with a standard deviation of 4 minutes. Assume that the two populations of completion times are normally distributed and that the population variances are equal. Construct a 95% confidence interval for the difference u, -, between the mean puzzle-solving times for Method A children (4,) and for Method B children (,). Then find the lower limit and upper limit of the 95% confidence interval. Carry your intermediate…

A researcher wonders whether the recession has changed variability in family size in his city. Before the recession, the mean was 3.7 and the standard deviation was 1.76. The researcher randomly selects 41 families from a population that is normally distributed. His sample has a mean of 3.1 and a standard deviation of 1.45. Test the claim that the standard deviation in size has changed at the αα=.05 significance level.

An educational psychologist is studying two methods of tutoring young children: Method A and Method B. She wants to test whether there is any difference in puzzle solving skills between children tutored by one method versus children tutored by the other. Independent samples of 10 children who were tutored using Method A and 11 children who were tutored using Method B were chosen at random. The Method A children took a mean of 40 minutes to solve a certain puzzle with a standard deviation of 6 minutes. The Method B children took a mean of 44 minutes to solve the same puzzle with a standard deviation of 7 minutes. Assume that the two populations of completion times are normally distributed and that the population variances are equal. Construct a 90% confidence interval for the difference u, - u, between the mean puzzle-solving times for Method A children ( u) and for Method B children (µ,). Then find the lower limit and upper limit of the 90% confidence interval. Carry your intermediate…