Hypothesistesting for population mean when standard deviation of the population is known1) ‘D’ size batteriesproduced by MNM Corporation have had a life expectancy of 87 hours. Because of animproved production process, the company believes that there has been an increasein the life expectancy of its ‘D’ size batteries. A sample of 36 batteries showedan average life of 88.5hours. Assume from past information that it is known that the standard deviation of the populationis 9 hours.a.Use a 0.01 level of significance, and test to determineif there has been an increase in the life expectancy of the ‘D’size batteries.b.What is the p-value associated with thesample results? What is your conclusion, based on the p-value?2) A carpet company advertises that itwill deliver your carpet within 15 days of purchase. A sample of 49 pastcustomers is taken. The average delivery time in the sample was 16.2 days.Assume the population standard deviation is known to be 5.6 days.a.State the null and alternativehypotheses.b.Using a critical value, test the nullhypothesis at the 5% level of significance.c.Using a p-value, test thehypothesis at the 5% level of significance.Hypothesistesting for population mean when standard deviation of the population isunknown1) From a population ofcans of coffee marked ’12 ounces,’ a sample of 25 cans is selectedand the contents of each can are weighed. The sample revealed a mean of 11.8ounces and a standard deviation of 0.5 ounces. Test to see if the mean of thepopulation is at least 12 ounces. (Assume the population is normallydistributed.) Use a .05 level of significance.2) A sample of 16 cookies is taken to test the claim that eachcookie contains lesserthan 9 chocolate chips. The average number of chocolate chips per cookie in the sample was 7.875 with a standard deviation of 1.Assume the distribution of the population is normal.a.State the null and alternativehypotheses.b.Using a critical value, test thehypothesis at the 1% level of significance.c.Using a p-value, test thehypothesis at the 1% level of significance.Hypothesistesting for population proportion1) A new soft drink is beingmarket tested. A sample of 400 individuals participated in the taste test and80 indicated they like the taste.a.At a 5% significance level, test todetermine if at least 22% of the population will like the new soft drink.b.Determine the p-value. 2) A student believes that no more than 20% of the studentswho finish a statistics course get an A. A random sample of 100 students wastaken. Twenty-four percent of the students in the sample received A’s.a.State the null and alternative hypotheses.b.Using a critical value, test thehypothesis at the 1% level of significance.c.Using a p-value, test thehypothesis at the 1% level of significance.
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