Question

A study for a shipping company, using a sample of 48 shipments gave a mean shipment weight of 2.83 tonnes and a standard deviation of 1.2 tonnes. The upper limit of a 95% confidence interval for the true mean weight of all shipments (in tonnes) is

a. 3.178

b. 3.169

c. 3.121

d. 3.115

Answer 1

A study for a shipping company using a sample of 48 shipments,gave a mean shipment weight of 2.83 tonnes and a standard deviation of 1.2 tonnes.

To find the upper limit of a 95% confidence interval for the true mean weight of all shipments.

The upper limit of the confidence interval is given by

m+(z*s)/sqrt(n)

where,

m is sample mean =2.83

s is sample standard deviation=1.2

n is sample size =48

and

for 95% confidence interval ,z-value=1.96

So,the upper limit is

2.83+(2.352/sqrt(48))

=3.169

Thus,(b) 3.169 is the correct answer.