Question

A researcher interested in Springfield citizens' shopping habits surveys a randomly selected group of 200 Walmart shoppers. 76% of those surveyed indicated that price was more important to them than where an item was produced. The researcher concluded that "about three quarters of the people in Springfield are more concerned with cost than where an item is made."This conclusion might be invalid because:

Answer 1

Answer and Explanation: The results of the survey would not be accurate to the whole of springfield, as the sample was not a random sample. A random sample is where each person in a given area (Springfield in this case) has an equal chance of being surveyed. In this case, only walmart shoppers were surveyed. Therefor, the results can only apply to shoppers at walmart, not the whole of Springfield.

Answer 2

Explanation:

Given that a researcher interested in Springfield citizens' shopping habits surveys a randomly selected group of 200 Walmart shoppers. 76% of those surveyed indicated that price was more important to them than where an item was produced.

`H_0: p=0.75\\H_a: p <0.75`

(One tailed test)

Sample proportion p = 0.76

p difference = 0.01

Std error =
`\sqrt{(pq)/(n) } =\sqrt{(0.75(0.25))/(200) } \\=0.0433`

Test statistic z = p difference / std error =
`(0.01)/(0.0433) =0.23`

p value = 0.409

Since p >0.05 we accept null hypothesis.

There is no statistical evidence to prove that proportion >3/4 or 0.75