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In a survey taken 10 years ago, it was found that 10% of customers of a supermarket brought along
their own shopping bags. A recent survey aimed to prove that the current percentage of customers
bringing along their own shopping bags is different from 10%. In the survey, it was found that 92 of
the 1 000 customers surveyed brought along their own shopping bags. We want to test the claim
that the current percentage is not 10%, at the 5% significance level.
(a) State the appropriate null and alternative hypothesis. (2)
(b) State and calculate the appropriate test statistic. (8)
(c) Determine the critical value of the test or the p–value of the test. (4)
(d) State whether or not you reject the null hypothesis, giving the reason. (3)
(e) Draw an appropriate conclusion. (3)
The following data give the distance travelled to work by a sample of employees.
14:8 12:9 13:2 15:0 13:5 12:1 14:8 16:1 15:1 16:2
Test at the 5% level of significance the claim that the average distance travelled is less than 15
kilometres if you are given a population standard deviation of 2:5 kilometers.
(a) State the null and alternative hypothesis. (2)
(b) Calculate the sample mean average distance travelled. (3)
(c) State and calculate the appropriate test statistic. (7)
(d) Determine the critical value of the test. (2)
(e) State whether or not you reject the null hypothesis, giving the reason. (3)
(f) Draw an appropriate conclusion. (3)
The net weight of cereal produced by Lucky Charms Ltd is normally distributed with a mean of 30 ounces and a standard deviation of 0.03 ounces. A box of cereal passes the quality test if its net weight is at least 29.94 ounces.
(a) Find the probability that a box of cereal randomly selected passes the quality test.
(b) A manager of Lucky Charms Ltd selects randomly n boxes of cereal for the quality test. He expects that the probability of no more than 20 boxes of cereal failing the
quality test is at least 0.95. What is the maximum number of boxes of cereal that he would select for the quality test? Justify the method that you use in the calculation.
A machine produces vitamin C tablets, the diameters of which are normally distributed with mean 10mm and a standard deviation of 0.1mm. A tablet is acceptable if its diameter lies between 9.81mm and 10.19mm. To pass a quality test, at least 90% of the tablets in a pack should be acceptable.
(a) Determine the probability that a tablet is acceptable. [5 marks]
(b) What is the probability that a pack of 20 tablets will pass the quality test? Use binomial probability distribution.
(c) What is the probability that a pack of 200 tablets will pass the quality test?
(d) If you have a choice of submitting a pack of 20 tablets or a pack of 200 tablets for the quality test, which one would you prefer and why?
mill employees who had previously checked them. If Smith , Jones, and
Brown, in that order, receive one of the three hats, list the sample space
points for the possible orders of returning the helmets, and find the
value m of the random variable M that represents the number of incorrect
matches.
In an accelerator center, an experiment needs a 1.41 cm thickaluminum cylinder. Suppose that the thickness of a cylinderhas a normal distribution with a mean 1.41 cm and a standarddeviation of 0.01 cm.
Identify which of these types of sampling is used: random, systematic, convenience, stratified, or cluster.
To determine her blood pressure, Carolyn divides up her day into three parts: morning, afternoon, and evening. She then measures her blood pressure at 4 randomly selected times during each part of the day
