Blog

A company considers the production process to be out of control when defects exceed 3%. In a random sample of 85 items, the defect rate is 5.9% but an employee claims that this is only a sample fluctuation and production is not really out of control. The company claims that this is evidence the production process is out of control and the defect rate is greater than 3%. Test the company’s claim at the .01 level of significance. The alternative hypothesis is p [alt] .03 (type , or =/) The p-value is [pvalue] (round to 4 decimal places) The test statistic is z=[test] (round to 2 decimal places) What is your conclusion about the company’s claim? [conclusion]  s = support the company’s claim r = reject the company’s claim f = fail to reject the company’s claim n = not enough evidence to support the company’s claim

Extra credit:  Earn 4 points extra credit The yield of a variety of wheat was measured on a series of small plots and was found to be approximately normal. The 2nd and 98th percentile were found to be 29 bushels/acre and 41 bushels/acre respectively. The standard deviation (bushels/acre) is approximately what? Hint:  Draw a sketch and mark the 2nd and 98th percentiles on the curve.  

Does the table below represent a valid probability distribution?

Find the following probability:  A test consists of 10 true/false questions. To pass the test a student must answer at least 6 questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?  Round your answer to 3 decimal places.  

Two types of flares are tested and their burning times (in minutes) are recorded.  The summary statistics are given below: Brand X Brand Y n=35 n=40 sample mean=19.4 min sample mean=15.1 s=1.4 min s=.8 min Use a .05 significance level to test the claim that the two samples are from populations with the same mean.  Assume that the two samples are independent simple random samples selected from normally distributed populations.  Do not assume the population standard deviations are equal.   The alternative hypothesis is U1 [alt] U2 (type , or =/) The test statistic is:  t=[test] (round to 3 decimal places) The p-value is:  [pvalue] The conclusion about the original claim is:  [claim] s = support the claim r = reject the claim f = fail to reject the claim n = not enough evidence to support the claim

Thirty pairs of data yield r = 0.474 and the regression equation . Also,  the mean of is 18.3.  What is the best predicted value of y for ? 

Use the given data to find the equation of the regression line. Round the final values to three decimal places, if necessary. x 2 4 5 6 y 7 11 13 20 The equation is y = [a] + [b]x

In studying the occurrence of genetic characteristics, the following sample data were obtained. The authors of the study expected each characteristic to occur with the same frequency.  At the 0.05 significance level, test the claim that the characteristics occur with the same frequency.  Characteristic A B C D E F Frequency 28 30 45 48 38 39  What is the test statistic?  [test] (round to 3 decimal places) What is the p-value? [pvalue] (round to 4 decimal places) What is your conclusion regarding the claim that the characteristics occur with equal frequency? [concl] Type r for reject Type s for support Type f for fail to reject Type n for not enough evidence to support

A researcher wishes to test the effectiveness of a flu vaccination. 150 people are vaccinated, 180 people are vaccinated with a placebo, and 100 people are not vaccinated. The number in each group who later caught the flu was recorded. The results are shown below. Vaccinated Placebo Control Caught the flu 8 19 21 Did not catch the flu 142 161 70 Use a 0.05 significance level to test the claim that getting the flu is independent of vaccination treatment. What is the p-value?   Round to 4 decimal places [pvalue] Does the data support that getting the flu is dependent or independent of treatment? [conclusion]  Type dependent or independent.  

Calculate the z-score for each test.  Round your answers to 2 decimal places. Test A:  A score of 82 on a test with a mean of 70 and a standard deviation of 8. [one] Test B:  A score of 82 on a test with a mean of 75 and a standard deviation of 4. [two] Based on the z scores, which test score is better?  [better]