Question

One study, based on responses from 1,023 selected teens, concluded that 43% of teens cite grades as source of pressure. Use a 0.05 significance level to test claim that fewer than half of all teens feel that grades are their greatest source of pressure.

A) formulate a null and alternative hypothesis

B) P value

C) Z value

D) conclusion

Answer 1

Given:

Sample size (n) = 1023

Level of signficance() = 0.05

Proportion of teens that cite grades as a source of pressure (p) = 0.43

a) The null and alternate hypothesis of the above question is as follows:

H_O : p = 0.50.

H_A : p < 0.50.

b and c) The p value is probability of the given model when the null hypothesis is true.

To calculate the p value, calculate the z value.

The above question is a left tail hypothesis. For level of significance = 0.05, the z value (z_0.05 ) is -1.65 for the left tail.

The above z value is computed from the standard normal table.

The p value is the probability of p(z < -1.65) as this is the rejection region.

p(z < -1.65) = 1 - p( z < 1.65)

= 1 - 0.9505 = 0.0495 = p value

d) From above, p value = 0.0495 and the level of significance () = 0.05.

As the p < , reject the null hypothesis.

Or, accept the alternate hypothesis.