A new drug is tested for serum cholesterol-lowering properties on six randomly selected volunteers. The serum cholesterol values are given in the following table.

(a) At 95% confidence level, test whether X and Y are independent.

(b) FInd the p-value.

(d) Interpret the usefulness of the model.

(e) State any assumptions you have made in solving the problem.

Solutions

Expert Solution

Solution

The given data:

(a) At 95% con dence interval, test whether X and Y are independent.

Since the test statistic value is included in rejection region, Hence we reject null hypothesis.

Therefore, X and Y are linearly related.

(b) Find p-value.

Therefore, p-value = 0:0373

For the given data we have:

(d) Interpret the usefulness of the model.

The least-squares regression line was selected as one that seems to fit the data reasonably well, and it minimizes the sum of squared errors.

(e) State any assumptions you have made in solving the problem.

We assumed that the pair (X; Y ) has bivariate normal probability distribution.

SUN BUNRA answered 1 year ago

Next > < Previous

Related Solutions

A new drug to treat high cholesterol is being tested by pharmaceutical company. The cholesterol levels...

A new drug to treat high cholesterol is being tested by pharmaceutical company. The cholesterol levels for 32 patients were recorded before administering the drug and after. The average difference in cholesterol levels (after - before) was 1.8 mg/dL with a standard deviation of 7.97 mg/dL. Using this information, the calculated 99% confidence paired-t interval is (-2.066, 5.666). Which of the following is the best interpretation of this interval? Question 11 options: 1) We are certain the average difference in...

To test the effectiveness of a new drug, a researcher gives one group of randomly selected...

To test the effectiveness of a new drug, a researcher gives one group of randomly selected individuals the new drug and another group of randomly selected individuals a placebo. The results are shown in the table below. Drug 32 (effective) 9 (ineffective) Placebo 12 (effective) 18 (ineffective) At 0.05, can the researcher conclude that the drug results differ from those of the placebo? (Show ALL steps including conditions).

A new drug for pain relief is being tested within a given palliative care population. The...

A new drug for pain relief is being tested within a given palliative care population. The new drug is being compared to an already approved pain relief drug that is commonly used in providing palliative care to patients who experience chronic severe pain. Assume the patients are asked to rate the pain on a scale from 1 to 10, and the data presented below was obtained from a small study designed to compare the effectiveness of the two drugs. Set...

Suppose a new standardized test is given to 97 randomly selected third-grade students in New Jersey....

Suppose a new standardized test is given to 97 randomly selected third-grade students in New Jersey. The sample average score Upper Y overbarY on the test is 56 points and the sample standard deviation, s Subscript Upper YsY, is 10 points. The authors plan to administer the test to all third-grade students in New Jersey. 1. The 95% confidence interval for the mean score of all New Jersey third graders is (round to two decimal places). 2. Suppose the same...

Suppose the following data are selected randomly from a population of normally distributed values. According to...

Suppose the following data are selected randomly from a population of normally distributed values. According to the U.S. Bureau of Labor Statistics, the average weekly earnings of a production worker in July 2011 were $657.49. Suppose a labor researcher wants to test to determine whether this figure is still accurate today. The researcher randomly selects 56 production workers from across the United States and obtains a representative earnings statement for one week from each. The resulting sample average is $670.76....

The Excel file BankData shows the values of the following variables for randomly selected 93 employees...

The Excel file BankData shows the values of the following variables for randomly selected 93 employees of a large bank. This real data set was used in a court lawsuit against discrimination. Let = monthly salary in dollars (SALARY), = years of schooling at the time of hire (EDUCAT), = number of months of previous work experience (EXPER), = number of months that the individual was hired by the bank (MONTHS), = dummy variable coded 1 for males and 0...

The Excel file BankData shows the values of the following variables for randomly selected 93 employees...

The Excel file BankData shows the values of the following variables for randomly selected 93 employees of a large bank. (A very similar data set was used in a court lawsuit against discrimination.) Let = monthly salary in dollars (SALARY), = years of schooling at the time of hire (EDUCAT), = number of months of previous work experience (EXPER), = number of months that the individual was hired by the bank (MONTHS), = dummy variable coded 1 for males and...

Given the following table of x and y values, test the claim that there is a...

Given the following table of x and y values, test the claim that there is a linear correlation. Use a .05 significance level. x|12 10 9 7 8 y | 182 169 155 140 144 For this particular problem, here’s the information you need to include: Step 1 Ho= Ha= Step 2 Signifcance level a= Step 3 Test: p-value: Step 4 Conclusion (Yes/No): Is there sufficient evidence to conclude that there is a linear correlation? 8. Find the regression equation...

The following sample of six measurements was randomly selected from a normally distributedpopulation: 2,5,−2,7,2,4a. Test the...

The following sample of six measurements was randomly selected from a normally distributedpopulation: 2,5,−2,7,2,4a. Test the null hypothesis that the mean of the population is 2 against the alternativehypothesis,μ <2.Useα=.05.b. Test the null hypothesis that the mean of the population is 2 against the alternativehypothesis,μ6= 2.Useα=.05.c. Find the observed significance level for each test

Suppose the following data are selected randomly from a population of normally distributed values. 41 51...

Suppose the following data are selected randomly from a population of normally distributed values. 41 51 43 48 44 57 54 39 40 48 45 39 40 Construct a 95% confidence interval to estimate the population mean.

Subjects