Question

1. A manager of the company would like to determine average delivery time of the products. A sample of 25 customers is taken. The average delivery time in the sample was four days with a standard deviation of 1.2 days. Suppose the delivery times are normally distributed.

1. Provide a 95 % confidence interval for the mean delivery time.
2. The manager claims that the average delivery time of their products does not exceed 3 days. Write the null and alternative hypothesis regarding to the claim of the manager.
3. Test the manager’s claim at 95 % confidence level.
4. Write the conclusion of your result

Answer 1

given data are:-

sample mean () = 4

sample sd (s) = 1.2

sample size (n) = 25

a).df = (n-1) = (25-1) = 24

t critical value for 95% confidence level, both tailed test be:-

[ using t distribution table, for df= 24,alpha=0.05,both tailed test]

the 95 % confidence interval for the mean delivery time is:-

b).hypothesis:-

our claim is the null hypothesis.

c).test statistic be:-

p value:-

[ in any blank cell of excel type =T.DIST.RT(4.1667,24) press enter]

decision:-

p value = 0.0002 <0.05 (alpha)

so, we reject the null hypothesis.

d).conclusion:-

there is not sufficient evidence to support the claim that the average delivery time of their products does not exceed 3 days at 0.05 level of significance.

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