In a test of running shoes. German sporting goods manufacturer, Derrunningzmitde

Question

In a test of running shoes. German sporting goods manufacturer, Derrunningzmitdershoessenhoffer, randomly selected 8 amateur runners to test two of its new shoe designs. The table shows how long the test shoes lasted before they were no longer usable. Test the null hypothesis that there is no difference in average life for the two shoes, using = 5%. Carrion Medical Insurance is concerned that the variation in recovery times (measured in weeks) for heart bypass patients at Mercy Hospital differs from the variation in recovery times for similar bypass patients at County Hospital. Eight random patients were selected from Mercy, and 12 random patients were selected from County. Past studies have found that recovery times are well-represented by a normal distribution. Recovery times for Mercy have a sample variance of 70.2. Recovery times for County have a sample variance of 28.4. Test the null hypothesis that the Mercy Hospital population variance is no greater than the County Hospital population variance. Use a significance level of 5%. The Environmental Protection Agency has conducted recent tests measuring peak pollution levels in various parts of Chicago. The average peak pollution readings for a sample of 21 days at each of 4 city locations are given in the table below, along with sample standard deviations a. Create an ANOVA table like the one shown below.

Explanation / Answer

From the given data we can calculate below

Below are the null and alternate hypothesis

p-value is 0.5845

As p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. This means from the given sample we can not conclude that there is difference in the life of two designs.

Given Data Sample 1 Sample 2 Name Design 1 Design 2 mean 14.3875 13.35 Sample size 8 8 Std. dev. 3.66 3.75

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