Question

According to a recent study, the mean number of people in a family (a married couple) in Canada is 4.80. A sociologist thinks this may not be the correct value for the city that she lives in. She examines a large apartment complex and interviews 100 randomly selected families (married couples) in the complex and obtains a mean of 4.64 persons per family. It is also known that the population standard deviation, σ, can be assumed to be 0.796.

You will test the sociologist’s claim using a two-sided test under three different methods and three different levels of significance. First, state the null and alternative hypothesis in symbols and words. Then test the hypothesis, make your decision and draw your conclusion using the following methods:

(a) A 98% confidence interval (1 H0/Ha, 2+1 for test = 4 marks)

(b) Classical testing with α = 5%

(c) The p-value method with a 10% level of significance. Also: how much evidence is there against the null hypothesis (very little, mild, strong, very strong or extremely strong)?

Requirement: (If the question is a hypothesis test question)

• State your null and alternative hypothesis with the correct symbols, the correct inequality sign, and in words

• Calculate the value of your test statistic

• For classical testing, give the critical value of z or t; for the p-value method, calculate the p-value (as an exact value OR as a range)

• Make your decision at the stated level of significance; if no level of significance is given, you need to decide how to proceed

• Finally, you need a conclusion. The conclusion should consist of THREE things: o Is the null hypothesis plausible of not? o Is your result (the value of the sample statistic) statistically significant or insignificant? o What is the conclusion of the test in the CONTEXT of the question?

Answer 1