Problem 1.A A sample of 21 observations was taken. The sample average (20.44) and the sample...

Problem 1.A

A sample of 21 observations was taken. The sample average (20.44) and the sample variance (2.90) were calculated. Take the hypothesis test by the three methods:

Ho µ = 21.5

Ha µ ≠ 21.5

to. Calculating the appropriate limits in terms of Xb for 95% reliability (sample average).

 

b. Calculate the limits in terms of the appropriate test statistic for 95% reliability and find the corresponding test statistic. 
 

c. Calculate the p-value for this hypothesis test.

 

Problem 1B

A study is carried out, in which 10 individuals participate, to investigate the effect of physical exercise on plasma cholesterol level. Before exercise, blood samples were taken to determine the cholesterol level of each individual. The participants then underwent an exercise program. At the end of the exercises blood samples were taken again and a second cholesterol level reading was obtained. The results are shown below:

 

Previous level: 182; 230; 160; 200; 160; 240; 260; 480; 263; 240

Back level: 190; 220; 166; 150; 140; 220; 156; 312; 240; 250

 

It is wanted to know if the physical exercise has reduced the cholesterol level for a confidence level of 95%. Establish the correct hypotheses and test.

Need A and B, Thanks!

Solutions

Expert Solution

1.A)

a) 95% CI for sample average is

( 19.6670, 21.2129)

b) t_cal=-2.8525

c) P-value is 0.0098

orchestra answered 2 years ago

Next > < Previous

Related Solutions

Problem 1.A A sample of 21 observations was taken. The sample average (20.44) and the sample...

Problem 1.A A sample of 21 observations was taken. The sample average (20.44) and the sample variance (2.90) were calculated. Take the hypothesis test by the three methods: Ho µ = 21.5 Ha µ ≠ 21.5 to: a.Calculating the appropriate limits in terms of Xb for 95% reliability (sample average). (10 pts) b. Calculate the limits in terms of the appropriate test statistic for 95% reliability and find the corresponding test statistic. (10 pts) c. Calculate the p-value for this...

A sample of 21 observations was taken. The sample average (18.44) and the sample variance (2.90)...

A sample of 21 observations was taken. The sample average (18.44) and the sample variance (2.90) were calculated. Take the hypothesis test by the three methods: Ho µ = 19.5 Ha µ> 19.5 to. Calculating the appropriate limit in terms of Xb for a reliability of 97.5% (sample average). (10 pts) b. Calculate the limit in terms of the appropriate test statistic for 97.5% reliability and find the corresponding test statistic. (10 pts) c. Calculate the p-value for this hypothesis...

A sample of 36 observations is selected from a normal population. The sample mean is 21,...

A sample of 36 observations is selected from a normal population. The sample mean is 21, and the population standard deviation is 5. Conduct the following test of hypothesis using the 0.05 significance level. H0: μ ≤ 20 H1: μ > 20 a). What is the decision rule? (Round your answer to 2 decimal places.) b). What is the value of the test statistic? (Round your answer to 2 decimal places.) c). What is the p-value? (Round your answer to...

A sample of 37 observations is selected from a normal population. The sample mean is 21,...

A sample of 37 observations is selected from a normal population. The sample mean is 21, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.02 significance level. H0: μ ≤ 20 H1: μ > 20 Is this a one- or two-tailed test? One-tailed test Two-tailed test What is the decision rule? Reject H0 when z > 2.054 Reject H0 when z ≤ 2.054 What is the value of the test statistic? (Round your...

1. A sample of 96 observations showed an average of 25 and a standard deviation of...

1. A sample of 96 observations showed an average of 25 and a standard deviation of 16. Construct the 90% confidence interval for the population mean. What is the lower limit of this interval? NOTE: WRITE YOUR ANSWER USING 4 DECIMAL DIGITS. DO NOT ROUND UP OR DOWN. 2. In a recent poll, from a sample of 140 likely voters, 65 answered they approve the way the president is handling his job. Compute the upper limit of the 95% confidence...

A sample of 500 observations taken from the first population gave x 1 = 305 ....

A sample of 500 observations taken from the first population gave x 1 = 305 . Another sample of 600 observations taken from the second population gave x 2 = 306 . Find the value of the test statistic z for p ^ 1 - p ^ 2 for H 0 : p 1 = p 2 versus H 1 : p 1 > p 2 . Will you reject the above mentioned null hypothesis at a significance level of...

We must show our work. 1. A sample of 81 observations is taken from a normal...

We must show our work. 1. A sample of 81 observations is taken from a normal population with a standard deviation of 5. The sample mean is 40. Determine the 80% confidence interval for the population mean. (Hint: Confidence Interval for a Population mean with population standard deviation (σ) known)

A simple random sample of 25 observations will be taken from a population that is assumed...

A simple random sample of 25 observations will be taken from a population that is assumed to be normal with a standard deviation of 37. We would like to test the alternative hypothesis that the standard deviation is actually more than 37. If the sample standard deviation is 40 or more, then the null hypothesis will be rejected (this called a decision rule). What significance level would this decision rule cause? If the population standard deviation is really 42, what...

For each of the following cases, assume a sample of n observations is taken from a...

For each of the following cases, assume a sample of n observations is taken from a normally distributed population with unknown mean μ and unknown variance σ2. Complete the following: i) Give the form of the test statistic. ii) State and sketch the shape of the prob. distribution of the test statistic when the null hypothesis is true. iii) Give the range of values of the test statistic which comprises the rejection region. iv) Sketch in the area(s) associated with...

If a sample containing 20 observations is taken from a normally distributed population and a 90%...

If a sample containing 20 observations is taken from a normally distributed population and a 90% confidence estimate for is needed, the appropriate t-score is (Specify your answer to the 3rd decimal.)

Subjects