Question 5

A researcher used a developed problem solving test to randomly select University first year students with a mean of 80 marks.The Science Professor tests this by using a sample of 50 first year students and got the mean of 75 marks with standard deviation of 15.With 95% confidence level, prove that the researcher's test is working perfectly.(Use traditional method)

Question 6

A sample of 40 objects is drawn from a population with standard deviation 37.93.The sample mean is 512.The null hypothesis that the mean is 500 is to be tested against the alternative that the mean is greater than 500 at a 0.01 significance level. Work out whether the or not the null hypothesis should be rejected or accepted and draw suitable conclusion.(Use traditional method)

Question 7

The average weight of all residents in Konoha is 168 kg.A nutritionist believes the true mean to be different.She measured the weight of 36 individuals and found the mean to be 169.5 kg with standard deviation of 3.9.

a.State the null and alternative hypotheses.

b.At a 95% confidence level, is there enough evidence to discard the null hypothesis? (Use the pvalue method)

Question 8

A factory manufactures cars with a warranty of 5 years on the engine and transmission.An engineer believes that the engine or transmission will malfunction in less than 5 years.He tests a sample of 40 cars and found the average time to be 4.8 years with standard deviation of 0.50.

a.State the null and alternative hypotheses

b.At a 2% significance level, is there enough evidence to support the idea that the warranty should be revised? (Use p-value method)