Question

The Australian Competition and Consumer Commission (ACCC) has released a report stating that across all supermarkets in Australia, the percentage increase in prices approximately follows a normal distribution with a mean increase of 4.2% and standard deviation of 0.9%.

If 16 supermarkets are randomly chosen, what is the probability that the average percentage increase is between 4% and 5%.

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Question 1 (4 points)

Calculate a 95% confidence interval of the mean expenditure of all male customers given that there were n = 131 males in the sample of 400, sample mean x = 50.1 and standard deviation s= 52.0.

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Question 2 (6 points)

Goodbuys is interested in determining the true proportion of all customers who rank the length of time they have to spend in queues as ‘excellent’. Given that 16.25% of the 400 customers who were surveyed gave a rating of ‘excellent’, calculate a 90% confidence interval for the true proportion.

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Interpret this confidence interval.

Question 3 (2 points)

State the assumptions you need to check before calculating the confidence interval in question 12.

Question 4 (4 points)

Suppose Goodbuy’s management want to know the true proportion of customers who rank the length of time they have to spend in queues as ‘excellent’ to within 3% with 95% confidence. How large a sample would need to be taken to achieve these requirements?

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Answer 1

the percentage increase in prices is normally distributed with 4.2% and 0.9%

the probability that the average percentage increase is between 4% and 5%. =

1)

We are 95% confident that the mean expenditure of all-male customers lie within the interval (41.1, 59.1)

2)

for 90% confidence

We are 90% confident that the true proportion of all customers who rank the length of time they have to spend in queues as ‘excellent’ lie within the interval (13.22% , 19.28%)

3) The sample should be random and the distribution to be normally and approximately normally distributed.

4) here an estimate of the proportion is not given so we assume p =0.5

margin of error: ME = 0.03

for 95% confidence

Sample size should be 1068