Question

Let p denote the proportion of students at a large university who plan to purchase a campus meal plan in the next academic year. For a large-sample z test of H0: p = 0.20 versus Ha: p < 0.20, find the P-value associated with each of the given values of the z test statistic.

(a)−0.53
(b)−0.96
(c)−1.91
(d)−2.28
(e)1.40

Answer 1

To find the P-values associated with each given z test statistic, we need to calculate the area under the standard normal curve. The P-value represents the probability that the test statistic takes a value as extreme as, or more extreme than, the observed test statistic under the null hypothesis.

Step-by-step explanation:

To find the P-values associated with the given values of the z test statistic, we need to calculate the area under the standard normal curve for a given z-value. The P-value represents the probability that the test statistic takes a value as extreme as, or more extreme than, the observed test statistic under the null hypothesis. Using a standard normal distribution table or a calculator with a standard normal distribution function, we can find the corresponding probabilities.

(a) For z = -0.53, the P-value is the area to the left of -0.53, which is approximately 0.2981.

(b) For z = -0.96, the P-value is the area to the left of -0.96, which is approximately 0.1664.

(c) For z = -1.91, the P-value is the area to the left of -1.91, which is approximately 0.0281.

(d) For z = -2.28, the P-value is the area to the left of -2.28, which is approximately 0.0119.

(e) For z = 1.40, the P-value is the area to the right of 1.40, which is approximately 0.0808.