Question

Important instructions: For all situations requiring a hypothesis test (z test, one-samplet test, one-sample variance test or two-sample t test), you must 1. Choose the appropriate test based on the information you are given 2. State null and alternative hypotheses 3. Choose a one or two tailed test and explain why you chose that test 4. Calculate the appropriate test statistic, showing all work neatly. This includes calculations of means, standard deviations, etc. 5. Draw the appropriate conclusions (i.e., do you reject or fail to reject Ho?) To help you know for sure which questions require this, I have marked the questions requiring these steps with an asterisk (*).You may assume data are normal and have equal variances-that necessary assumptions have been fulfilled.

Answer 1

Solution:

Here, we have to use Chi square test for the population variance.

The null and alternative hypotheses are given as below:

H₀: σ² ≥ 50 versus H_a: σ² < 50

This is a lower tailed (one tailed) test.

We assume level of significance = α = 0.05

The test statistic formula is given as below:

Chi square = (n – 1)*S^2/ σ²

From given data, we have

n = 10

S = 10

df = n – 1 = 10 – 1 = 9

Chi square = (10 - 1)*10^2/50

Chi square = 9*10^2/50

Chi square = 18

Test statistic = 18

Lower critical value = 3.3251

(by using Chi square table or excel)

P-value = 0.9648

(by using Chi square table or excel)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is not sufficient evidence to conclude that variance of scores is significantly less than 50.