Question

We are interested in finding out the proportion of adults in the United State who cannot cover a $400 unexpected expense without borrowing money or going into debt. In a simple random sample of 765 adults in the United States, 322 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?


(b) What parameter is being estimated?


(c) What is the point estimate for the parameter?


(d) What is the name of the statistic can we use to measure the uncertainty of the point estimate?


(e) Compute the value from part (d) for this context.


(f) A cable news pundit thinks the value is actually 50%. Should she be surprised by the data?


(g) 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 ^p, does the resulting value change much?

Answer 1

Answer:

Step-by-step explanation:

given that we are interested in finding out the proportion of adults in the United State who cannot cover a $400 unexpected expense without borrowing money or going into debt.

Sample size = 765

Favour = 322

a) The population is the adults in the United State who cannot cover a $400 unexpected expense without borrowing money or going into debt

b) The parameter being estimated is the population proportion P of adults in the United State who cannot cover a $400 unexpected expense without borrowing money or going into debt.

c) point estimate for proportion = sample proporiton = $\frac{322}{765} \\=0.4209$

d) We can use test statistic here as for proportions we have population std deviation known.

d) Std error = 0.01785($\sqrt{\frac{pq}{n} }$

Test statistic Z = p difference / std error

f) when estimated p is 0.50 we get Z = -4.43

g) Is true population value was 40% then

Z = 1.17 (because proportion difference changes here)