QUESTION 1: A company sells packets of biscuits that they claim, on average, contains at least 20 g biscuits in each packet. They admit that their claim is wrong (and will refund any money) if a sample of 40 has a mean less than 19.8 g. If the standard deviation is 0.5 g,
a) Formulate the appropriate null and alternative hypotheses, and determine the type of test.
b) If the test is conducted at α = 0.05, determine the critical value that specify the rejection region, then complete this sentence: Reject H¬0 if test statistic is ___________________
c) Find the probability of a Type I error.
d) Find the probability of a Type II error and determine the power of test if the true mean is 19.5 g.
QUESTION 2: A researcher wishes to determine whether the average amount of bleaching agent in a 1kg packet of brand X wheat flour exceeds that of brand Y. Fifteen 1kg packets of wheat flour for each brand were selected at random. It is found that on average, X contains 5% bleaching agent with a standard deviation of 0.3 and Y contains on average, 4% bleaching agent content with standard deviation of 0.5.
a) Obtain the point estimate of the mean difference of the bleaching agent content in a packet of 1kg wheat flour.
b) Determine the sampling distribution for the mean difference of the bleaching agent in a 1kg packet of wheat flour.
c) Formulate the appropriate null and alternative hypotheses to be tested.
d) Calculate the test statistics for the test.
e) Interpret your findings at 5% level of significance.