Question

A recent survey in the N.Y. Times Almanac indicated that 48.8% of families own stock. A broker wanted to determine if this survey could be valid. He surveyed a random sample of 250 families and found that 142 owned some type of stock. At the 0.05 significance level, can the survey be considered to be accurate?

Short answer

The survey does not appear to be accurate.

Step-by-step solution

State the null and alternate hypothesis. we have to conduct hypothesis test if families of N.Y take 48.8% of families own stock or not, on average. 

$H_0:p=0.488;H_a:p\ne 0.488$

Calculate the p-value using the normal distribution for proportions: 

$p-value=0.0114$

In one to two complete sentences, explain what the p-value means for this problem. If the null hypothesis is true (the proportion is 0.488), then there is a 0.0114 probability that the sample (estimated) proportion is 0.568 or more.

Compare α and the p-value:Indicate the correct decision (“reject” or “do not reject” the null hypothesis), the reason for it, and write an appropriate conclusion, using complete sentences.

alpha	decision	reason for decision
0.05	Do not reject the null hypothesis.	$p-value>0.05$

Conclusion: At the 5% level of significance, there is enough evidence to conclude that 48.8% of families own stocks.

accuracy of the survey

The survey does not appear to be accurate.