Question

1. A local newspaper claims that 60% of the items advertised in its classified advertisement section are sold within one week of the first appearance of the advertisement. To check the validity of the claim, the newspaper randomly selects advertisements from last year’s classified advertisement and contacts the people who place the advertisements. They found that 13 of the 35 items were sold within one week.

1. What is the estimate of the proportion of items sold within a week of the first appearance of the advertisement?
2. What is the standard error of the sample proportion?
3. If the claim is true, what is the approximate distribution of the sample proportion for a random sample of 35 items? (Provide all features of the distribution).
4. Based on this claim, for a random sample of 35 items, it is likely to observe 13 or fewer items sold within a week? Calculate the exact probability.

Answer 1

(a) The estimate of the proportion of items sold = 13/35 = 0.37

(b) The standard error of the sample proportion = √p(1-p)/n = √0.60(1-0.60)/35 = 0.083

(c) n*p = 35*0.60 = 21 10

n*(1 - p) = 35*(1 - 0.60) = 14 10

This is a normal distribution.

(d) The test statistic, z = (p̂ - p)/√p(1-p)/n

z = (0.37 - 0.60)/√0.60(1-0.60)/35

z = -2.76

The p-value is 0.0029.

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