Stats homework please help

Question

1.Find the 𝑃 −value for the indicated hypothesis test for a population proportion with the given standardized test statistic (𝑧 −score).

Two-tailed test, 𝑧 = 2.13

(a) 0.0166

(b) .0332

(c) 0.0083

(d) 0.0664

2.Find the z-critical value necessary to construct a confidence interval at the 86% level of

a) .52

(b) -1.48

(c) 1.48

(d) 1.08

3.Find the margin of error for the given confidence interval: (54.9,59.5)

(a) 2.3

(b) 57.2

(c) 5.6

(d) 4.6

Answer 1

Hi Ariel,

The p-value for a given z-value is the probability of having a z-score greater in magnitude than the given z-value. In terms of area under a graph, this corresponds to the area in the tail to the right of a positive z-value, or to the left of a negative z-value. For a two-sided test, we include the area in both tails.

So for a two-sided test, with z = 2.13, the p-value would correspond to the area right of 2.13 and left of -2.13. Since these areas are the same, we can just say two times the area to the left of -2.13, which we can determine with a calculator function, or a z-table.

If you need more detail than the above, please consider scheduling a session to discuss the topic further.

Regards,

John R.