A random sample of 1562 undergraduates enrolled in marketing

A random sample of 1,562 undergraduates enrolled in marketing courses was asked to respond on a scale from one (strongly disagree) to seven (strongly agree) to the proposition: “ Advertising helps raise our standard of living”. The population mean response was 4.27 with a standard deviation of 1.32.

Perform a hypothesis test at a 1% significance level that the population mean response is not equal to 4.

Note: “You can use either the Critical value approach or the p-value approach.”

Solution

n=1562

Mean mu = 4

Standard Deviation SD = 1.32

X-bar = 4.27

alpha =0.01

Null Hypothesis : mu = 4
Alternate Hypothesis: mu !=4

z = (X-bar - mu)/(SD/sqrt(n))

=(4.27 - 4)/(1.32/sqrt(1562)) = 127.8481

= 8.08

This is two tailed test,

P-value = ~1

Since P-value > 0.01

Failed to reject null hypothesis .