A hotel asked its customers to rate their stay as Good, Average or Poor. The following contingency table shows the frequ

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A hotel asked its customers to rate their stay as Good, Average
or Poor. The following contingency
table shows the frequency of each rating as well as the age group
of the customers.
(i) Show whether there is any evidence of a significant
association between age group and
rating of customers. Use
  0.02 . (10 marks)
(ii) Construct a 98% confidence interval for the true proportion of
customers giving good rating.
Thus, interpret the answer. (5 marks)
(iii) It is claimed that the proportion of customers who are 50
years old and above and give poor
rating to the hotel is more than 5%. Can the claim be supported at
5% level of significance?
(10 marks)
(b) A standard intelligence test has been given to the university
students for several years and it is
assumed that the scores are normally distributed with an average of
70 and a standard deviation of
10. A group of 30 university students obtained a mean grade of 65
in the examination this year. Is
this year’s university students inferior in intelligence to the
past years’ university students using
1% level of significance? (10 marks)
(c) (i) A manufacturer of light bulbs believes that one particular
brand of light bulbs has a lifetime
of 30000 hours. A simple random sample of 100 of the light bulbs is
taken and the mean
lifetime is found to be 29500 hours with a standard deviation of
1270 hours. Test the
manufacturer's claim at 5% level of significance. (10 marks)
(ii) Find a 96% confidence interval estimate for the mean lifetime
of all light bulbs produced by
this manufacturer. (5 marks)