Mathematics: Each student was asked to record and report the amount of money they spent on text books in a semester. The sample of 130 students resulted in the average of $422 and a standard deviation of $57. Find a 99% confidence interval for the mean amount of money spent by collage students on textbooks

I think the answer is 7.4 x 10-4mm, because a CD is pretty small....

Each student was asked to record and report the - id5953257, elissiashontelbrown

Ответ:

taykola

23.01.2022

Mathematics

(409.36, 434.64)

Step-by-step explanation:

When population standard deviation is unknown and sample is not so large , then the formula to find the confidence interval for population mean is given by :-

$\overline{x}\pm t^*\dfrac{s}{\sqrt{n}}$

, where $\overline{x}$ = sample mean , n = sample size , s= sample population standard deviation, t*= two tailed critical value.

As , per given , $\overline{x}=\$422$ , s=$57, n=130

For 99% confidence , $\alpha=0.01$

By t-distribution table , t-value for $\alpha/2=0.005$ (two tailed) and df =129 [∵df=n-1] would be

t*=2.6145

Now , the 99% confidence interval for the mean amount of money spent by collage students on textbooks will be :

$422\pm (2.6145)\dfrac{57}{\sqrt{139}}$

$422\pm (2.6145)(4.834677)$

$422\pm 12.640263$

$(422- 12.640263,\ 422+12.640263)\\\\=(409.359737,\ 434.640263)\approx(409.36,\ 434.64)$

Hence, a 99% confidence interval for the mean amount of money spent by collage students on textbooks will be (409.36, 434.64).

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Each student was asked to record and report the amount of money they spent on text books in a semester. The sample of 130 students resulted in the average of $422 and a standard deviation of $57. Find a 99% confidence interval for the mean amount of money spent by collage students on textbooks

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