A researcher claim that the average yearly consumption of so

A researcher claim that the average yearly consumption of soft drink per person is 52 gal. In a sample of 50 randomly selected people, the mean of the yearly consumption 52.9 gal. The standard deviation of the population is 3.5 gal. On the basics of the P-value, is the researcher claim valid at a =0.10?

Solution

Let mu be the population mean

The test hypothesis:

Ho: mu=52 (i.e. null hypothesis)

Ha: mu not equal to 52 (i.e. alternative hypothesis)

The test statistic is

Z=(xbar-mu)/(s/vn)

=(52.9-52)/(3.5/sqrt(50))

=1.82

It is a two-tailed test.

So the p-value= 2*P(Z>1.82) =0.0688 (from standard normal table)

Since the p-value is less than 0.1, we reject the null hypothesis.

So we can not conclude that the average yearly consumption of soft drink per person is 52 gal.