Question 2 The energy consumption of refrigerators sold in a country is checked

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Question 2 The energy consumption of refrigerators sold in a country is checked and appliances are given a star rating to guide consumers who are about to make purchases. The consumption in kWh per annum is also displayed for each model on the govenment website. Suppose a consumer organisation wants to estimate the actual electricity usage of a model of refrigerator that has an advertised energy usage of 439 kWh per annum. It tests a random sample of 18 fridges and finds a sample mean usage of 445 and a sample standard deviation of 40 a) Assuming that the energy usage in the population is normally distributed, construct a 95% confidence interval estimate of the population mean energy usage for this model of refrigerator b) Do you think that the consumer organisation should accuse the manufacturer of producing fridges that do not meet the advertised energy consumption? Explain

Explanation / Answer

Let the confidence interval be (a,b)

n = 18 s = 40 x' = 445 z = 1.96

a) a = x' - zs/n

= 445 - 1.96*50/18

= 421.9012

b = x' + zs/n

= 445 + 1.96*50/18

= 468.0988.

The confidence interval is(421.9012, 468.0988).

b) Since the value of 439 lies within the confidence interval, the consumer organization should not accuse the manufacturer of producing fridges that do not meet the advertised energy consumption.

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