Question

A researcher wishes to​ estimate, with 95​% ​confidence, the population proportion of adults who eat fast food four to six times per week. Her estimate must be accurate within 5​% of the population proportion. ​(a) No preliminary estimate is available. Find the minimum sample size needed. ​(b) Find the minimum sample size​ needed, using a prior study that found that 26​% of the respondents said they eat fast food four to six times per week. ​(c) Compare the results from parts​ (a) and​ (b)

QUESTION TO ANSWER : ​(a) What is the minimum sample size needed assuming that no prior information is​ available? n=?

Answer 1

(a)

The following information has been provided: (1)Margin of Error E = 0.05 (2)Level of significance α=0.05 (3)Since no estimate of the population proportion p is provided, we use the estimate p = 0.5 (which corresponds to the worst-case scenario). The critical value for the significance level α=0.05 is Zc =1.96. This can be found by using either Excel or by using the normal probability table. The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error: Therefore, the sample size needed to satisfy the condition is n ≥ 384.1459, and it must be an integer number, we conclude that the minimum required sample size is

(b)

The following information has been provided: (1)Margin of Error E = 0.05 (2)Level of significance α=0.05 (3)The provided estimate of the population proportion p is p = 0.26 The critical value for the significance level α=0.05 is Zc =1.96. This can be found by using either Excel or by using the normal probability table. The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error: Therefore, the sample size needed to satisfy the condition is n ≥ 295.6387, and it must be an integer number, we conclude that the minimum required sample size is

(C)

The sample size when no estimate of population proportion is available (a) is always going to be higher when we have some sort of estimate available (b). This is because we take p to be 0.5 in Case 1 which will lead to the highest sample size possible.

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