Question

In a sample of 50 households, the mean number of hours spent on social networking sites during the month of January was 45 hours. In a much larger study, the standard deviation was determined to be 8 hours. Assume the population standard deviation is the same. What is the 95% confidence interval for the mean hours devoted to social networking in January?

Answer 1

The 95% confidence interval ranges from 8 to 45 hours. <--- not this one.
The 95% confidence interval ranges from 40.13 to 45.78 hours.
The 95% confidence interval ranges from 43.87 to 46.13 hours.
The 95% confidence interval ranges from 42.78 to 47.22

Answer 2

For 95% confidence interval, the critical z value is z = 1.96 approx. This is something where it's found in a table or you use a calculator


Now you'll use these formulas to get the lower bound (L) and the upper bound (U) of the confidence interval


\[\Large L = \bar{x} - z*\frac{s}{\sqrt{n}}\]
\[\Large U = \bar{x} + z*\frac{s}{\sqrt{n}}\]

In this case,
\[\Large \bar{x} = 45\]
\[\Large z \approx 1.96\]
\[\Large s = 8\]
\[\Large n = 50\]

Answer 3

Okay, and when I solve those formulas what would I do?

Answer 4

Let's compute the lower bound L

\[\Large L = \bar{x} - z*\frac{s}{\sqrt{n}}\]
\[\Large L = 45 - 1.96*\frac{8}{\sqrt{50}}\]
\[\Large L = ???\]
I'll let you do the last step. Tell me what you get.

Answer 5

43.04 * 8/sqrt50

Answer 6

then sqrt of 50 is 7.07106781

Answer 7

so we would have 43.04 * 1.13137085

Answer 8

You don't subtract yet. Subtraction is the last thing you do

Answer 9

follow PEMDAS

Answer 10

Oh okay so we would multiply 8/sqrt of 50 by -1.96? how would I do that

Answer 11

\[\Large L = \bar{x} - z*\frac{s}{\sqrt{n}}\]
\[\Large L \approx 45 - 1.96*\frac{8}{\sqrt{50}}\]
\[\Large L \approx 45 - 1.96*\frac{8}{7.07106781}\]
\[\Large L \approx 45 - 1.96*1.13137085\]
\[\Large L \approx 45 - 2.217486866\]
\[\Large L \approx 42.782513134\]
\[\Large L \approx 42.78\]
Hopefully that makes sense?

Answer 12

Before i saw this I was about to say if it was 42.782513134198987

Answer 13

good, you got it

Answer 14

what is the upper bound U?

\[\Large U = \bar{x} + z*\frac{s}{\sqrt{n}}\]

Answer 15

So would the answer be D since it is the only one with that number?

Answer 16

yes, as practice tell me what you get for the upper bound U

Answer 17

okay

Answer 18

before I continue, is this correct? 45+2.217486866

Answer 19

yes it is

Answer 20

okay so would it be 47.217486866

Answer 21

correct

Answer 22

side note: `2.217486866` is the approximate margin of error

Answer 23

Thank you so much :)

Answer 24

Oh okay, gotcha. Thanks for all of your help

Answer 25

lower bound = (estimate) - (margin of error)
upper bound = (estimate) + (margin of error)

Answer 26

no problem