Question

A manager of an e-commerce 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.

For an effective parental skill study, a researcher asked: How many hours do your kids watch the television during a typical week in Barcelona? The mean of 100 Kids (ages 6-11) spend about 28 hours a week in front of the TV. Suppose the study follows a normal distribution with standard deviation 5.

1. Estimate the mean of all kids (ages 6-11) in Barcelona, using 99% confidence interval. (show all the calculations)
2. Write the conclusion of your result

Answer 1

(a)

Here n=25, =4, s=1.2

Let the population mean be

The test statistic follows t distribution with df=n-1=24

Hence the 95% confidence interval is (3.50464,4.49536)

(b)

The null and the alternative hypotheses are given by

(c)

The test statistic is given above as

The critical value of -t0.05,24 is given by -1.711 [from the Biometrika table]

As the observed value is more than the critical value, then we fail to reject the null hypothesis at 5% level of significance and hence we conclude that the average time is 3days.

Here n=100,   

Let the population mean be

The test statistic follows standard Normal distribution .

Hence the 99% confidence interval is (26.712,29.288)

(b)

It can be concluded at 1% level of significance that the mean hours spent in front of TV by all kids in Barcelona lies in between 26.712 and 29.288.

Hopefully this will help you. In case of any query, do comment. If you are satisfied with the answer, do comment. Thanks.