Suppose a recent nationwide survey showed that 35% of American college students have traveled outside of the USA. But a well known university believes its students have traveled abroad more than the national rate of 35%. A random sample of 100 students from this university had 42 students who have traveled outside the USA. A hypothesis test is then conducted to determine if we can believe that, statistically, more of this university's students have traveled abroad. Using these numbers, what is the value of the test statistic for this hypothesis test

Question

Mathematics

Duncan Armstrong

2 December, 18:29

Suppose a recent nationwide survey showed that 35% of American college students have traveled outside of the USA. But a well known university believes its students have traveled abroad more than the national rate of 35%. A random sample of 100 students from this university had 42 students who have traveled outside the USA. A hypothesis test is then conducted to determine if we can believe that, statistically, more of this university's students have traveled abroad. Using these numbers, what is the value of the test statistic for this hypothesis test

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Answers (1)

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Celeste Bowen · Answer 1

Step-by-step explanation:

We would set up the hypothesis test.

For the null hypothesis,

p = 0.35

For the alternative hypothesis,

p > 0.35

This is a right tailed test considering the > in the alternative hypothesis.

Considering the population proportion, probability of success, p = 0.35

q = probability of failure = 1 - p

q = 1 - 0.35 = 0.65

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 42

n = number of samples = 100

P = 42/120 = 0.42

We would determine the test statistic which is the z score

z = (P - p) / √pq/n

z = (0.42 - 0.35) / √ (0.35 * 0.65) / 100 z = 1.48