From a simple random sample of 14 shoppers surveyed, the sample mean of money spent for holiday gifts was 145 dollars with a sample standard deviation of 11 dollars. Read and provide each of the following: The sample size?=, the sample mean ?-=, the sample standard deviation ?=, he confidence level CL=%.

UkusakazaL

UkusakazaL

Answered question

2021-08-08

From a simple random sample of 14 shoppers surveyed, the sample mean of money spent for holiday gifts was 145 dollars with a sample standard deviation of 11 dollars. We wish to construct a 99% confidence interval for the population mean of money spent for holiday gifts.
Read carefully the text and provide each of the following:
The sample size ?=,
the sample mean ?,
the sample standard deviation ?=, NKS the confidence level CL=%.

Answer & Explanation

OlmekinjP

OlmekinjP

Beginner2021-08-09Added 1 answers

Step 1
Given that
Sample size (n)=14
Mean money spent (x)=$145= Sample mean
Sample standard deviation (s)=$11
Confidence level =99%
Level of significance (α)=10.99=0.01
Note: Here, population standard deviation is unknown and sample size is small (n<30) so, small sample test t-test is used: NKS Degrees of freedom (df)=(n1)=141=13
t critical value at df=13, α=0.01 at one-tailed is 2.650 (tcrit=2.65)
Step 2
we know that
confidence interval (C.I.)=x±tcritxsn
C.I.=145±2.65x1114=145±7.79=(1457.79, 145+7.79)
(137.21, 152.79)
Required confidence interval for population mean of money spent for holiday gifts is ($137.21, $152.79)

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?