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ON TWO (8marks) a) The weights of full boxes of a certain kind of cereal are nor

ID: 1113431 • Letter: O

Question

ON TWO (8marks) a) The weights of full boxes of a certain kind of cereal are normally distributed with a standard deviation of 0.27 g. A sample of 18 randomly selected boxes produced a mean weight of 987g Find a 95% confidence interval for the true rmean weight of a box of this cereal. (4marks) ) A company producing light bulbs finds that mean life span of the population of bulbs is 1200 hours with a standard deviation of 125hrs. A sample of 100 bulbs produced in a lot is found to have a mean life span of 1150hrs. Test whether the difference between the population and sample means is statistically significant at 5% level of significance (4marks) UESTION THREE 10marks) A random sample of 500 students completed a questionnaire on how often they took par in some form of exercise. They gave a response of 'never', 'sometimes those asked, 52% were females of whorm 10% never exercised and 35% exercise regularly. Of the males, 12.5% never exercised and 55% sometimes exercised. Test, at the 5% level of significance, whether or not there is any association betw gender and the amount of exercise. State your hypotheses clea (10marks) a) or 'regularly'

Explanation / Answer

a)

Z=(X-m)/s/(n)^1/2

CI(X) = (mean(m)-z*sd/n, mean(m)+z*sd/n)

Where m is the mean=9.78g

Z is the value of standard variate at 95% = 1.96

SD is the stanfdard deviation = 0.27g

N is the number of observations = 18

CI(x) = (9.87 -1.96*0.27/18 , 9.87 +1.96*0.27/18)

CI(x) = (9.87 -0.124, 9.87+0.124)

CI(x) = (9.746, 9.994)