Final answer:
A broker's survey on the ownership of stocks by families is tested against a published survey result using a two-proportion z-test at a 0.05 significance level. The null hypothesis is that there is no significant difference in proportions. Rejecting or not rejecting the null hypothesis depends on whether the p-value is less than 0.05.
Step-by-step explanation:
A recent survey has indicated that 48.8% of families own stock. A broker has conducted his own survey with a random sample of 250 families and found that 142 owned some type of stock. We must conduct a hypothesis test to determine if the broker's results significantly differ from the survey or if the broker's survey can be considered accurate.
To proceed, we use a two-proportion z-test at a 0.05 significance level. The null hypothesis (H0) states that the proportion of families that own stock is equal to 48.8%, and the alternative hypothesis (Ha) claims that the proportion is different from 48.8%.
The test statistic would be calculated using the formula for the difference between two proportions and then compared with the critical values from the standard normal distribution or by using the p-value method. If the calculated p-value is less than the chosen significance level of 0.05, we reject the null hypothesis, concluding that there is a significant difference. However, if the p-value is greater, we do not reject the null hypothesis and the broker's survey can be considered accurate within the context of the test.