Question 2 – (Please answer both a and b)

A recent survey showed that from a sample of 500 packages delivered by a Postal Service, 480 were delivered on time.

a) Construct a 95% confidence interval for the proportion of all packages that are delivered on time by the Postal Service. 

b) The manager of the Postal Services claims that 98 percent of their mail are delivered on time. Test at the 1% significance level to determine whether the true proportion is less than 98 percent.

A recent survey showed that from a sample of 500 packages delivered by a Postal Service, 480 were delivered on time.

b) The manager of the Postal Services claims that 98 percent of their mail are delivered on time. Test at the 1% significance level to determine whether the true proportion is less than 98 percent. Answer this using the T-distribution table ONLY.

Question 2.

In 2002, the average duration of incoming telephone calls to a furniture store was 9.4 minutes. The manager wants to perform a test to determine whether this average duration
of incoming calls has changed. Twenty calls to the store was randomly selected and the mean duration was 10.2 minutes with standard deviation 4.8 minutes. Assuming that the duration of incoming telephone calls to a furniture store is normally distributed,
a) Use a 1% level of significance to test whether the mean duration of incoming calls to the store had changed. Calculate using the Statistical T Distribution Table ONLY.