Question

Using the information regarding the proportion of work time linguists study a new language, choose the correct conclusion for this hypothesis test. H0:p=0.10 ; Ha:p>0.10 The p-value for this hypothesis test is 0.09. The level of significance is α=0.025 Select the correct answer below: A) There is sufficient evidence to conclude the proportion of work time linguists study a new language is more than 10%.

B) There is NOT sufficient evidence to conclude the proportion of work time linguists study a new language is more than 10%.
C) There is sufficient evidence to conclude the proportion of work time linguists study a new language is more than 90%.
D) There is NOT sufficient evidence to conclude the proportion of work time linguists study a new language is more than 90%.

Answer 1

B) There is NOT sufficient evidence to conclude the proportion of work time linguists study a new language is more than 10%.

Explanation:

Given that:

the null hypothesis is;

`H_o : p =0.10`

the alternative hypothesis is:

`H_a : p >0.10`

The p - value for the hypothesis is 0.09

The level of significance ∝ = 0.025

The Decision rule is that to reject the null hypothesis if the p-value is less than the level of significance ∝.

Conclusion: We fail to reject the null hypothesis because the p-value is greater than the level of significance , therefore:

There is NOT sufficient evidence to conclude the proportion of work time linguists study a new language is more than 10%.