Question

A researcher asks a large population of people (several thousand) how many times per year they attend religious services. The mean number is 17 and the standard deviation is 7. You recruit a random sample of 144 people and ask them the same question. The mean for the sample is 17.75. First, compute the standard error of the mean. Next, conduct a z test and use Table Z to find the area of the normal curve that falls beyond the z score you obtained.

Answer 1

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

H0: µ = 17 versus Ha: µ ≠ 17

This is a two tailed test.

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 17

Xbar = 17.75

σ = 7

n = 144

α = 0.05

Critical value = -1.96 and 1.96

(by using z-table or excel)

Z = (17.75 - 17)/[7/sqrt(144)]

Z = 1.2857

P-value = 0.1985

(by using Z-table)

P-value > α = 0.05

So, we do not reject the null hypothesis