Company A is trying to sell its website to Company B. As part of the sale, Compa

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. Company B is concerned that the mean time is significantly less than 10 minutes. Company B collects the times (in minutes) below for a sample of 18 users. Assume normality.

Time
5.2
4.6
5.6
3.1
5.2
0.2
2.3
1.4
11
0.6
0.7
1.8
5.9
4.6
1.1
0.5
2.3
6.3

Time
5.2
4.6
5.6
3.1
5.2
0.2
2.3
1.4
11
0.6
0.7
1.8
5.9
4.6
1.1
0.5
2.3
6.3

Time
5.2
4.6
5.6
3.1
5.2
0.2
2.3
1.4
11
0.6
0.7
1.8
5.9
4.6
1.1
0.5
2.3
6.3

Conduct the appropriate hypothesis test for Company B using a 0.03 level of significance.

a) What are the appropriate null and alternative hypotheses?

H0: = 10 versus

Ha: > 10H0: = 10 versus Ha: < 10    

H0: x = 10 versus Ha: x 10

H0: = 10 versus Ha: 10

    
b) What is the test statistic? Give your answer to four decimal places

c) What is the critical value for the test? Give your answer to four decimal places.

d) Which of the following is the appropriate conclusion?

1)Reject the claim that the mean time is 10 minutes because the test statistic is smaller than the critical point.

2)Reject the claim that the mean time is 10 minutes because the test statistic is larger than the critical point.    

3)Fail to reject the claim that the mean time is 10 minutes because the test statistic is larger than the critical point.

4) Fail to reject the claim that the mean time is 10 minutes because the test statistic is smaller than the critical point.

Explanation / Answer

Solution:

Will perform one sample t test in R

Code:

time <- c(
5.2,
4.6,
5.6,
3.1,
5.2,
0.2,
2.3,
1.4,
11,
0.6,
0.7,
1.8,
5.9,
4.6,
1.1,
0.5,
2.3,
6.3
)
View(time)
t.test(time,mu=10,alternative = "less",conf.level = 0.97)

Output:

ata: time
t = -9.8479, df = 17, p-value = 9.687e-09
alternative hypothesis: true mean is less than 10
97 percent confidence interval:
-Inf 4.803467
sample estimates:
mean of x
3.466667

ANSWERS:

Conduct the appropriate hypothesis test for Company B using a 0.03 level of significance.

a) What are the appropriate null and alternative hypotheses?

= 10 versus Ha: < 10

b) What is the test statistic? Give your answer to four decimal places

T=-9.8479

Solutionc:

c) What is the critical value for the test? Give your answer to four decimal places.

t=2.015

Solutiond:

|t cal|=|-9.8479|=9.8479

tcal>tcrit

Reject Null hypothesis

2)Reject the claim that the mean time is 10 minutes because the test statistic is larger than the critical point.   

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