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In a survey of 1051 adults, a poll asked, "Are you worried or not worried about having enough money for retir
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Question 1139536: Can someone please help my son with solving this question:
In a survey of 1051 adults, a poll asked, "Are you worried or not worried about having enough money for retirement?" Of the 1051 surveyed, 599 stated that they were worried about having enough money for retirement. Construct a 95% confidence interval for the proportion of adults who are worried about having enough money for retirement.
A 95% confidence interval for the proportion of adults who are worried about having enough money for retirement is Answer by jim_thompson5910(35256) (Show Source):
Of that sample size, x = 599 said they were worried, so
is a good estimate of the population proportion of people worried about having enough money for retirement.
The notation is read as "p-hat". Basically it's the letter "p" but with a "hat" on top so to speak. This is to help separate it from the regular letter "p" which is the population proportion; while is the sample proportion.
Let's compute the standard error which I'll call "SE" for short. see note below
note: we do not use p here as we don't know the population proportion. If we knew the population proportion then we wouldn't need a confidence interval (since a confidence interval is used to estimate the population proportion). We can say that p-hat is an unbiased estimator of p.
Now onto the margin of error, which I'll abbreviate as "ME". We'll need the z critical value. At 95% confidence, the critical z value is approximately z = 1.960; this value is found using a calculator or a table.
I used this table to find the z critical value. Scroll to the bottom of the page to locate the row that starts with Z. Then locate the column that has "95%" at the very bottom. The value just above this is 1.960. A table similar to this should be found in the appendix section of your statistics textbook.
The margin of error is then added and subtracted from the p-hat value, as the p-hat value is the best estimate of p. The p-hat value is the center of the confidence interval. The margin of error tells us how spread out or how wide the interval is.
L = lower boundary of confidence interval
The upper boundary is nearly identical, but instead we add this time.
Answer: (0.54, 0.60)
This answer is approximate rounded to two decimal places.
Interpretation: We are 95% confident that the true proportion p is between 0.54 and 0.60, meaning that we're 95% confident that the proportion of people worried about having enough money for retirement is between 54% and 60%.
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