Question

You are considering investing in a company. The company claims for the past few years the average monthly return on such an investment has been $870 with a standard deviation of $50. You sample 30 investors and determine the sample average return to be $855. Using a .05 level of significance you will test to determine if there is evidence that the true average return is different from $870. What are your critical values? +- 1.65 +- 2.045 +-1.96 +-1.65   

Answer 1

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

The null and alternative hypotheses are given as below:

Null hypothesis: H0: the true average return is $870.

Alternative hypothesis: Ha: the true average return is different from $870.

H0: µ = 870 versus Ha: µ ≠ 870

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 = 870

Xbar = 855

σ = 50

n = 30

α = 0.05

Critical value = -1.96 and 1.96

(by using z-table or excel)

Z = (855 - 870)/(50/sqrt(30))

Z = -1.6432

P-value = 0.1003

(by using Z-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that the true average return is different from $870.