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boards rejected per batch is 5 7 with a variance of 1 4 The factory manager suspects that due to a change in the molding process the variance has increased She tests a random sample of 10 batches produced using the new process the number of circuit boards rejected per batch has a sample variance of 2 5 Assume the numbers of circuit boards rejected per batch using the new process follow a normal distribution Is there sufficient evidence to conclude that the population variance is greater than 1 4 To answer complete the parts below to perform a hypothesis test Use the 0 10 level of significance a State the null hypothesis and the alternative hypothesis that you would use for the test Ho H 0 O O Oso 020 0 0 Chi square Distribution Step 1 Enter the number of degrees of freedom Step 3 Enter the test statistic Round to 3 decimal places Step 2 Select one tailed or two tailed O One tailed O Two tailed S b Perform a chi square test and find the p value Here is some information to help you with your chi square test n The value of the test statistic is given by 1 2 Step 5 Enter the p value Round to 3 decimal places X The p value is the area under the curve to the right of the value of the test statistic Step 4 Shade the area represented by the p value 5 O O 034 02 0 1 10 15 c Based on your answer to part b choose what can be concluded at the 0 10 level of significance about the population variance in the number of circuit boards rejected per batch using the new process Since the p value is less than or equal to the level of significance the null hypothesis is rejected So there is enough evidence to conclude that the variance is greater than 1 4 Since the p value is less than or equal to the level of significance the null hypothesis is not rejected So there is not enough evidence to conclude that the variance is greater than 1 4 Since the p value is greater than the level of significance the null hypothesis is rejected So there is enough evidence to conclude that the variance is greater than 1 4 O Since the p value is greater than the level of significance the null hypothesis is not rejected 30 X 5

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