Question

In: Statistics and Probability

(a) Food Dragon and Delivery Woo are two main food delivery companies in Hong Kong. Suppose...

(a) Food Dragon and Delivery Woo are two main food delivery companies in Hong Kong. Suppose the delivery time of these two companies both follow a normal distribution. A random sample of size 10 is selected from each of the food deliveries.

Sample Size mean(mins) standard deviation(mins)

Food Dragon 10 20 5

Delivery Woo 10 15   6

Assuming the delivery times of both companies are normal with equal variances, find the 90% confidence interval for the difference between the mean delivery time of Food Dragon and Delivery Woo. [8marks]

(b) A random sample of 1000 citizens from Macau have been tested for the anti-body for the coronavirus. It was found that 150 of these citizens has the anti-body for the coronavirus. Find a 93% confidence interval for the true population proportion of citizens in the Macau with the anti-body. [5 marks]

(c) An engineer wants to find out the concentration of carbon monoxide (µg/m3 ) emitted by a newly invented car. The engineer collected 14 observations in a randomly chosen period.

68, 54, 32, 80, 50, 40, 60, 60, 55, 40, 42, 50, 60, 43

Construct a 95% confidence interval for the mean concentration of carbon monoxide. Assume that the concentrations of CO are normally distributed. [7 marks]

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orchestra answered 2 years ago
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