Final answer:
To test if a smaller proportion of American families own stocks this year compared to ten years ago, set up a hypothesis test using the historical value as the null hypothesis and compute the sample proportion based on new data. Calculate the Z-score and find the P-value, and if it is less than 0.05, reject the null hypothesis.
Step-by-step explanation:
The question asks about conducting a hypothesis test to determine if a smaller proportion of American families own stocks or stock funds this year compared to ten years ago. To test this hypothesis, we would set the null hypothesis (H0) to state that the current proportion of families owning stocks or stock funds is equal to the historical value of 53%, while the alternative hypothesis (Ha) would claim that the current proportion is less than 53%.
Based on the provided sample of 280 families, with 148 owning stocks or stock funds, we can calculate the sample proportion, which is 148/280 = 0.5286. To find the P-value, we would use the normal distribution as an approximation for the binomial distribution, since our sample size is sufficiently large. Then by standardizing the sample proportion, we calculate the Z-score and find the corresponding P-value from the Z-distribution table or using statistical software. The P-value would indicate the probability of observing a proportion of stock-owning families as extreme as the sample proportion, under the assumption that the null hypothesis is true.
If the P-value is less than the significance level (commonly set at 0.05), we would reject the null hypothesis and conclude that there is statistically significant evidence that a smaller proportion of American families own stocks or stock funds this year compared to ten years ago.