Project #30336 - Statistics Assignment

1.     A revenue department is under orders to reduce the time small business owners spend filling out pension form ABC-5500. Previously the average time spent on the form was 6.3 hours. In order to test whether the time to fill out the form has been reduced, a sample of 53 small business owners who annually complete the form was randomly chosen, and their completion times recorded. The mean completion time for ABC-5500 form was 6.1 hours with a standard deviation of 2.6 hours. In order to test that the time to complete the form has been reduced, state the appropriate null and alternative hypotheses.

2.     A method currently used by doctors to screen women for possible breast cancer fails to detect cancer in 17% of women who actually have the disease. A new method has been developed that researchers hope will be able to detect cancer more accurately. A random sample of 74 women known to have breast cancer were screened using the new method. Of these, the new method failed to detect cancer in ten. Specify the null and alternative hypotheses that the researchers wish to test.

 

3.      I want to test null hypotheses : p = .7 vs. hypotheses : p ≠ .7 using a test of hypothesis. If I concluded that p is .7 when, in fact, the true value of p is not .7, then I have made what type of error?

 

4.     Consider a test of H0 : μ ≤ 9 versus  Ha: μ > 9. State the rejection region in terms of the              z-statistic when α = 0.01.

 

5.     How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 66 tissues during a cold. Suppose a random sample of 10,000 people yielded the following data on the number of tissues used during a cold:    We want to test the alternative hypothesis   : μ < 66. State the correct rejection region for α= .05.

 

6.     We have created a 99% confidence interval for μ with the result (LL = 10, UL = 15). What conclusion should we make if we test  at

 

7.     For the given value of α and observed significance level (p-value), indicate whether the null hypothesis would be rejected. α = 0.01, p-value = 0.05.

 

8.     A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful only if the average time spent on a delivery does not exceed 30 minutes. The owner has randomly selected 17 customers and delivered pizzas to their homes in order to test whether the mean delivery time actually exceeds 30 minutes. What assumption is necessary for this test to be valid?

 

9.     A company claims that 9 out of 10 doctors (i.e., 90%) recommend its brand of cough syrup to their patients. To test this claim against the alternative that the actual proportion is less than 90%, a random sample of 100 doctors was chosen which resulted in 83 who indicate that they recommend this cough syrup. Compute the test statistic in this problem.

 

10.   Identify the observed level of significance for the test summarized on the screen below and interpret its value.

            

1-propZTest

prop<.75

z=-2.323790008

p=.0100683519

B=.6

n=45

Subject Mathematics
Due By (Pacific Time) 05/07/2014 12:00 am
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