Statistics help | Mathematics homework help

 

The quiz has two portions:

 

Multiple Choice (8 problems, 32 points). Show work/explanation as appropriate.

 

Short Answer (3 problems, 38 points) Show work.

 

 

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 

 

  1. (4 points) If the P-value of a hypothesis test comparing two means was 0.25, what can you conclude? (Select all that apply):

 

A. You can accept the null hypothesis

 

B. There was a significant difference between the means

 

C. You failed to reject the null hypothesis

 

D. There did not appear to be significant difference between the means

 

         

 

 

 

  1. (4 points) Imagine a researcher wanted to test the effect of the new drug on reducing blood pressure. In this study, there were 50 participants. The researcher measured the participants’ blood pressure before and after the drug intake. If we want to compare the mean blood pressure from the two time periods with a two-tailed t test, how many degrees of freedom are there?

 

           A. 49

 

           B. 50

 

           C. 99

 

           D. 100

 

 

 

 

 

  1.  (4 points) When sample size increases, ____

 

      A. Power increases a great degree at first, reaches its peak, and then slowly decreases

 

      B. Power decreases a great degree at first, reaches its lowest point, and then slowly increases

 

      C. Power increases a great degree at first, and then increases slowly

 

      D. Power decreases a great degree at first, and then decreases slowly

 

 

 

  1. (4 points) α=0.05 for a two-tailed test. Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis.

 

  A. ±1.768

 

        B. ±1.764

 

        C. ±1.96

 

        D. ±2.575

 

 

 

  1. (4 points) In a sample of 47 adults selected randomly from one town, it is found that 9 of them have been exposed to a particular strain of the flu. Find the P-value for a test of the claim that the proportion of all adults in the town that have been exposed to this strain of the flu is 8%.

 

  A. 0.0024

 

        B. 0.0524

 

        C. 0.0228

 

        D. 0.0048

 

 

 

 

 

 

 

 

 

  1.  (4 points) For a simple random sample, the size is n=17, σ is not known, and the original population is normally distributed. Determine whether the give conditions justify testing a claim about a population mean µ.

 

     A. Yes

 

           B. No

 

 

 

  1. (4 points) A medical researcher claims that 20% of children suffer from a certain disorder. Indentify the type I error for the test.

 

        A. Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 20% when the percentage is actually 20%.

 

        B. Reject the claim that the percentage of children who suffer from the disorder is equal to 20% when that percentage is actually 20%.

 

        C. Fail to reject the claim that the percentage of children who suffer from the disorder is equal to 20% when that percentage is actually different from 20%.

 

        D.Reject the claim that the percentage of children who suffer from the disorder is different from 20% when that percentage really is different from 20%.

 

 

 

  1. (4 points) The duration of telephone calls directed by a local telephone company: σ=4.2 minutes, n=500, 97% confidence. Use the confidence level and sample data to find the margin of error E.

 

        A. 0.018 min

 

        B. 0.008 min

 

        C. 0.408 min                              

 

        D. 0.087 min

 

 

 

 

 

 

 

 

 

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.  Express percents as decimals. Round dollar amounts to the nearest cent.

 

  1. (10 points) List below are the ages in years of randomly selected race car drivers. Use a 0.05 significant level to test the claim that the mean age of all race car drivers is greater than 30 years.

 

32       32    33    33    41    29    38    32   33   23   27   45   52    29   25

 

 

 

10. (10 points) It is commonly accepted that the mean temperature of human is 98.6oF. Yours truly has nothing better to do but measured the temperatures of 26 colleagues 1 to 4 times daily to get a total of 123 measurements. The collected data yielded a sample mean of 98.4oF and a sample standard deviation of 0.7oF. Is the mean temperature of his colleagues less than 98.6oF at the 0.01 significance level? Justify your answer with the proper statistics.

 

 

11. (18 points)The recommended daily allowance (RDA) of cobalamine (Vitamin B12) for growing teens is 2.4 µg (micrograms). It is generally believed that growing teens are getting less than the RDA of 2.4 µg of cobalamine daily.

 

A not-to-be-named Pharmaceutical (ntbnP) peddles dietary supplements around the country. It is claimed by ntbnP representatives that by taking their vitamin supplement, teens will have the RDA of cobalamine. FDA is going to take on ntbnP to show that the supplement comes short of providing teens with the recommended RDA.

 

FDA managed to collect with a 24-hour period blood sample of 10 randomly selected teens around the country. The amounts of cobalamine (in µg) determined in these 10 randomly selected teens are given as follow:

 

1.85 2.35 1.87 1.90 1.37 2.35 2.55 2.28 1.95 2.49

 

Based on their national experience, FDA assumes that the the population standard deviation of cobalamine in teens to be 0.56 µg.

 

Now, you are asked to weigh in on the dispute between FDA and ntbnP.

 

a. (3 points) Given the above information, what kind of hypothesis test will you conduct? z-test, t-test, χ2-test, F-test, or Ω-test? Please explain.

 

 

 

b. (3 points) What will be the null hypothesis, the alternative hypothesis, and, hence, the “tailedness” of the test (left-tailed, right-tailed, or two-tailed)?

 

 

 

c. (3 points) What is be the corresponding test statistics?

 

 

d. (3 points) What is the corresponding p-value of the hypothesis test?

 

 

e. (3 points) What kind of conclusion can you draw from the hypothesis test you have just performed? Of course, representatives of ntbnP would like to have the conclusion skewed to their advantage. And so would the officials from FDA. What would you do if you are representing ntbnP? But, if you are representing FDA, how would you present your argument?

 

 

f. (3 points) But, wait. What if FDA actually does not know the population standard deviation in this case, would you conduct your hypothesis test different? Just in case that you are going to perform the hypothesis different, what would you do instead?

 

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