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

The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.013 inches. What proportion of bolts will have a diameter greater than 0.32 inches?  Note:  give your answer as a proportion – a decimal rounded to 4 decimal places.  

In a game, you have a probability of winning $85 and a probability of losing $4.  What is your expected value?  Round your answer to two decimal places.

In one town, 44% of all voters are Democrats.  If two voters are randomly selected for a survey, find the probability they are both Democrats.  Round to the nearest thousandth.

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 ? 

At the 0.025 significance level, test the claim that the four brands have the same mean if the following sample results have been obtained. Brand A Brand B Brand C Brand D 17 18 21 22 20 18 24 25 21 23 25 27 22 25 26 29 21 26 29 35 29 36 37 What is the p-value? [pvalue] round to 4 decimal places Do the means appear to be the same? [conclusion] yes or no

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

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]

Use the given values of n and p to find the maximum usual value μ + 2σ for a binomial distribution. Round your answer to one decimal place. n = 246, p = 0.15