Question

An appliance manufacturer company TED Ltd claims to have developed a new oven that consumes an average of no more than 250 W. Power consumption for t ovens is normally distributed with a standard deviation of 18 W. A consumer group suspects the actual average is more than 250 W. They take a sample of 20 ovens and calculate the average consumption to be 260 W.

1. State the null and alternative hypotheses for the consumer group to do their test. (2 marks)
2. What conclusion can you draw from the hypothesis test using a = .05? (3 marks)
3. Please identify the similarities and differences between Standard normal distribution and Student’s t distribution.(3 marks)

Answer 1

a) The Hypotheses are:

b) Hypothesis testing:

Since the population standard deviation is known hence we assume it as normally distributed and Z score can be applicable for hypothesis testing instead of t-distribution as the sample size is less than 30.

Test statistics:

P- value:

The p value computed using Z table shown below at Z score calculated above is 0.0066.

Conclusion:

Since the P value <<0.05 level of significance hence we reject the null hypothesis and conclude that there is enough evidence to support the claim that actual average is more tha 250.

c) The Standard normal distribution is applicable only when we know that the population from which we are sampling is normally distributed and we also have the access to the parameter, while if the population distribution parameter is unknown also the population standard deviation is not known and the sample size is less than 30 then t-distribution is applicable.

It is also assumed that of the mean and standard deviation of sample is equal to the mean and standard of population hence the T distribution approaches normal distribution.

Also of the sample size is increased from 30 the sample distribution approaches normal distribution