Question

A transect is an archaeological study area that is mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance . In a different section of Chaco Canyon, a random sample of 25 transects gave a sample variance for the number of sites per transect. Use an alpha = 0.1 to test the claim that the variance in the new section is greater than 37.9. Given 0.05 < P-Value < 0.1, will you reject or fail to reject the null hypothesis of independence? ​ Select one:

a. Since the P-Value is less than the level of significance, we reject the null hypothesis that the variance is equal to 37.9. At 0.1 level of significance, we conclude that the variance is greater than 37.9.

b. Since the P-Value is less than the level of significance, we fail to reject the null hypothesis that the variance is greater than 37.9. At 0.1 level of significance, we conclude that the variance is equal to 37.9.

c. Since the P-Value is greater than the level of significance, we fail to reject the null hypothesis that the variance is greater than 37.9. At 0.1 level of significance, we conclude that the variance is equal to 37.9.

d. Since the P-Value is greater than the level of significance, we fail to reject the null hypothesis that the variance is equal to 37.9. At 0.1 level of significance, we conclude that the variance is greater than 37.9.

e. Since the P-Value is less than the level of significance, we fail to reject the null hypothesis that the variance is equal to 37.9. At 0.1 level of significance, we conclude that the variance is greater than 37.9.

Answer 1

ANS- (a)

State the null and alternate hypotheses

Ho: σ² = 37.9 ;

H₁: σ² > 37.9 ;

Given

= 0.1 and 0.05 < p-Value < 0.1,

NOTE that significance level for a given hypothesis test is a value for which a p-value less than or equal to is considered statistically significant. Typical values for are 0.1, 0.05, and 0.01. These values correspond to the probability of observing such an extreme value by chance.

When you perform a hypothesis test in statistics, a p-value helps you determine the significance of your results. ... The p-value is a number between 0 and 1 and interpreted in the following way: A small p-value (typically ≤ ) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

• In this case p-Value is less than 0.1 where 0.1 is (level of significance).

it means it gives a strong evidence against the null hypothesis.hence we reject the null hypothesis that the variance is equal to 37.9. At 0.1 level of significance, we conclude that the variance is greater than 37.9.