Question

In a random sample 762 adults in the United States, 326 say they could not cover a $400 unexpected expense without borrowing money or going into debt. (a) What population is under consideration in the data set? all adults who were surveyed all adults in the United States who could cover the expense all adults in the United States all adults all adults in the United States who could not cover the expense (b) What parameter is being estimated? the average number of U.S. adults who could not cover a $400 expense without borrowing money or going into debt the proportion of U.S. adults who could cover a $400 expense without borrowing money or going into debt the exact number of U.S. adults who could not cover a $400 expense without borrowing money or going into debt the proportion of U.S. adults who could not cover a $400 expense without borrowing money or going into debt the average number of U.S. adults who could cover a $400 expense without borrowing money or going into debt (c) What is the point estimate for the parameter? (Round your answer to three decimal places.) 0.428 (d) What is the name of the statistic can we use to measure the uncertainty of the point estimate? sample proportion sample mean standard error O sample size (e) Compute the value from part (d) for this context. (Round your answer to four decimal places.) (f) A cable news pundit thinks the value is actually 50%. Should she be surprised by the data? (Round your answer to two decimal places.) A value of 0.50 is standard errors way from the point estimate, so she should be surprised. (9) Suppose the true population value was found to be 40%. If we use this proportion to recompute the value in part (e) using p = 0.4 instead of hat p_{1} does the resulting value change much? Yes No

Answer 1

(a) The population under consideration in the dataset is all adults in the United States who could not cover a $400 expense without borrowing money or going into debt.

(b) The parameter being estimated is the proportion of U.S. adults who could not cover a $400 expense without borrowing money or going into debt.

(c) The point estimate for the parameter is 0.428.

(d) The statistic to measure the uncertainty of the point estimate is the standard error.

(e) The value of the standard error for this context is 0.0161.

(f) A cable news pundit thinking the value is actually 50% would be surprised, as 0.50 is several standard errors away from the point estimate.

(g) If the true population value was 40%, using this proportion for the standard error computation would result in a significant change.

Step-by-step explanation:

(a) The data set considers all adults in the United States who could not cover a $400 expense without borrowing money or going into debt.

(b) The parameter being estimated is the proportion of U.S. adults with this financial inability.

(c) The point estimate is calculated as 326/762 ≈ 0.428.

(d) The standard error is a measure of the uncertainty of the point estimate.

(e) Compute the standard error using the formula for proportions, resulting in approximately 0.0161.

(f) If the pundit thinks the value is 50%, she should be surprised as it deviates significantly from the point estimate.

(g) If the true population value is 40%, using this proportion for the standard error would lead to a substantial change in the result.