Question

Hypothesis Test Yajvin is an analyst working for Big Gains Financial Advisory Services Ltd. (BGF). He was analyzing the weekly returns (calculated on annual basis) of 25 companies drawn from the infrastructure industry. He knows that the population standard deviation (σ) is 3.4 percent. He selected 32nd week of the 2017-18 fiscal and calculated the average weekly returns and the sample average turned out be 7.2 percent. (Select the option that is nearest to the correct answer) He was testing the null hypothesis as stated below: H0: μ = 8.00% HA: μ ≠ 8.00 % What is the value of σ_X ̅ ? What is range of sample means within which the null hypothesis cannot be rejected, given α =0.05? Calculate the probability of committing Type II error, if the alternate value for μ is 9.0 percent, given α =0.05. Yajvin felt that those companies which have too high or too low returns (based on his own definition of outliers) should be removed from his sample. Consequently he dropped 10 of the 25 companies from his sample. He also decided to change α to 10% and carry out a one-sided test H0: μ≤ 8.00% HA: μ > 8.00 % What are the possible values of the sample mean within which the above null hypothesis cannot be rejected? What is the p-value corresponding to the hypothesis test (Question 2 above) with respect to the sample of 25 companies and a sample mean of 7.2 percent?

Answer 1

The standard error of mean is

--------------

So range of sample means within which the null hypothesis cannot be rejected is from 6.667 and 9.333.

--------------------

Type II error:

-----------------------------------

So range of sample means for which the null hypothesis cannot be rejected is from -infinity to 9.125.

----------------------------------