Question

An overnight package delivery service has a promotional discount rate in effect this week only. For several
years the mean weight of a package delivered by this company has been 10.7 oz. A random sample of 12
packages mailed this week has sample mean weight 11.81 oz with standard deviation 2.24 oz. Test the claim
that the mean weight of all packages mailed this week is greater than 10.7 oz. Use a 1% significance level.

For each hypothesis test please provide the following information:
(a) State the null and the alternate hypotheses.
(b) Identify the sampling distribution to be used: the standard normal distribution or the student’s t distribution.
Find the critical values.
(c) Sketch the critical region and show the critical value(s) on the sketch.
(d) Compute the z or t value of the sample test statistic and show its location on the sketch of part (c).
(e) Based on your answers to parts (a) through (e) decide whether to reject or not reject the null hypothesis at
the given significance level. Explain your conclusion in simple terms.

Answer 1

a. Here claim is that the mean weight of all packages mailed this week is greater than 10.7 oz

So hypothesis here is vs

b. As n<30 and population standard deviation is not known so we will use t distribution

c, t critical value for right tailed at 11 df is 2.718

d. Test statistics is

e. As t critical value is greater than test statistics we fail to reject the null hypothesis