Answer to Question #227290 in Statistics and Probability for Investor

Question

A monthly income investment scheme exists that promises variable monthly returns. An investor will invest in it only if he is assured of an average $180 monthly income. He has a sample of 300 months' returns which has a mean of $190 and a standard deviation of $75. should he or she invest?

Answer 1

Solution:

H₀: Null Hypothesis: mean = 180

H₁: Alternative Hypothesis: mean > 180

Using Standardized Test Statistics,

$z=\dfrac{\bar X-\mu}{\sigma/\sqrt n}=\dfrac{190-180}{75/\sqrt {300}} \\z=2.309$

Our rejection region at 5% significance level is Z> Z_0.05 = 1.645.

Since Z= 2.309 > 1.645, the null hypothesis can be rejected.

So, mean > 180, so the investor can invest.