statistics

Problem 2

A medical researcher treats high cholesterol with a new drug that reduces cholesterol after two months.

The manufacturer's claim is that the drug will reduce cholesterol levels (on average) by 60mg/dL, but the researcher thinks it might be more than that and sets up the test:  The researcher then takes a sample of 30 individuals and finds that the average decrease in cholesterol level is 65mg/dL with a sample standard deviation of 12 mg/dL after two months of taking the drug. 

What is the null hypothesis in the Cholesterol drug test?

Select one:

a. The drug reduces the cholesterol level by 65mg/dL, on average

b. The drug reduces the cholesterol level by 12mg/dL, on average

c. The drug reduces the cholesterol level by 30mg/dL, on average

d. The drug reduces the cholesterol level by 60mg/dL, on average

What is the alternative hypothesis in the Cholesterol drug test?

Select one:

a. The drug reduces cholesterol by more than 65mg/dL

b. The drug reduces cholesterol by more than 12mg/dL

c. The drug reduces cholesterol by more than 60mg/dL

d. The drug reduces cholesterol by  65mg/dL

Calculate the p-value associated with the Cholesterol drug test. Round your answer to four decimal places.

Answer:

Does your result provide significant evidence to reject the null hypothesis at the 1% level of significance?

Select one:

True

False

Choose the correct conclusion of the test of hypothesis for the Cholesterol drug

Select one:

a. There is evidence at the 5% level of significance to suggest that the average reduction in cholesterol level is equal to 60mg/dL

b. There is significant evidence at the 5% level of significance to suggest that the average reduction in cholesterol level is more than 60mg/dL

c. There is evidence at the 5% level of significance to suggest that the average reduction in cholesterol level is equal to 65mg/dL

d. There is not enough evidence at the 5% level of significance to suggest that the average reduction in cholesterol level is more than 60mg/dL

Please copy and paste your R code for the Cholesterol level hypothesis test here.

Also, explain in your words the reasons for your answers regarding the conclusion of this test.

Pobleme 3

There's a traffic light near your house, and you collect a random sample of how long the light is red. These are the times (measured in seconds):   40   38    44    42    39    42    39

Compute the sample mean for the traffic lights. Round your answer to two decimal places.

Answer

Compute the sample standard deviation for the traffic lights. Round your answer to two decimal places.

Answer:

(14): Assuming that the population is approximately normal, compute a 95% confidence interval for the average amount of time that the traffic light is red.What is the lower bound of this interval?

Round your answer to two decimal places

Answer:

15: Assuming that the population is approximately normal, compute a 95% confidence interval for the average amount of time that the traffic light is red.

What is the upper bound of this interval?

Round your answer to two decimal places

Answer:

16: Please copy and paste your R code for the Traffic lights problem.

Also, explain in your words the meaning of the confidence interval.

Problems 4:

A sample of size 49 has sample mean 35 and sample standard deviation 14. Construct a 96% confidence interval for the population mean using this information.

What is the margin of error?

Round your answer to two decimal places.

Answer:

Please copy and paste your R code for the large sample size confidence interval problem.

Also, explain in your words the meaning of the confidence interval.