Company A is trying to sell its website to Company B. As part of the sale, Compa
ID: 3341245 • Letter: C
Question
Company A is trying to sell its website to Company B. As part of the sale, Company A claims that the average user of their site stays on the site for 10 minutes. To test this claim Company B collects the times (in minutes) below for a sample of 11 users. Assume normality.
4.9
6.1
0.4
10.5
18.3
3.7
4.2
6.5
0.1
Construct a 91% confidence interval for the true mean time spent on the web site.
a) What is the lower limit of the 91% interval? Give your answer to three decimal places. Enter 0 if your lower limit is less than 0.
b) What is the upper limit of the 91% interval? Give your answer to three decimal places.
c) Based on this data, do you believe the claim made by Company A?
Yes because 10 is not inside the interval.
Yes because 10 is inside the interval.
No because 10 is not inside the interval.
No because 10 is inside the interval.
d) Which of the following assumptions should be checked before constructing the above confidence interval?
the data need to be skewed
the data need to follow a normal distribution
the data need to have small variance
the data need to follow a t distribution
Explanation / Answer
We can analyse this in R , the snippet is as follows
data <- c(4.9,
6.1,
0.4,
10.5,
18.3,
3.7,
4.2,
6.5,
0.1)
## 91% confidence interval
## upperlimit
mean(data) + qnorm(1-0.09/2)*sd(data)/length(data)
## lower limit
mean(data) - qnorm(1-0.09/2)*sd(data)/length(data)
The results are
5.029665,7.125891
Based on this data, do you believe the claim made by Company A?
Yes because 10 is not inside the interval.
Yes because 10 is inside the interval.
No because 10 is not inside the interval. as the confidence interval is 5.029665,7.125891
No because 10 is inside the interval.
d) Which of the following assumptions should be checked before constructing the above confidence interval?
the data need to be skewed
the data need to follow a normal distribution
the data need to have small variance
the data need to follow a t distribution
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