Answer:
We conclude that the population mean is not equal to 17.
Step-by-step explanation:
We are given the following in the question:
Population mean, μ = 17
Sample mean, = 14.12
Sample size, n = 40
Alpha, α = 0.05
Population standard deviation, σ = 4
First, we design the null and the alternate hypothesis
We use Two-tailed z test to perform this hypothesis.
a) Formula:
Putting all the values, we have
b) P-value can be calculated from the standard z-table.
P-value = 0.0000
c) Since the p-value is less than the significance level, we reject the null hypothesis and accept the alternate hypothesis. Thus, the population mean is not equal to 17
d) Now,
e) Rejection Rule:
We reject the null hypothesis if it is less than lower critical value and greater than the upper critical value
If the z-statistic lies outside the acceptance region which is from -1.96 to +1.96, we reject the null hypothesis.
f) Since the calculated z-stat lies outside the acceptance region, we reject the null hypothesis and accept the alternate hypothesis. Thus, the population mean is not equal to 17.