Answer:
Step-by-step explanation:
We would set up the hypothesis test.
For the null hypothesis,
p = 0.5
For the alternative hypothesis,
p < 0.5
Considering the population proportion, probability of success, p = 0.5
q = probability of failure = 1 - p
q = 1 - 0.5 = 0.5
Considering the sample,
P = 42/100 = 0.42
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
n = 400
z = (0.42 - 0.5)/√(0.5 × 0.5)/400 = - 3.2
Recall, population proportion, p = 0.5
We want the area to the left of 0.5 since the alternative hypothesis is lesser than 0.5. Therefore, from the normal distribution table, the probability of getting a proportion < 0.5 is 0.00069
So p value = 0.00069
Since alpha, 0.05 > than the p value, 0.00069, then we would reject the null hypothesis.
Therefore, there is significant evidence to conclude that that less than 50% of people under the age of 25 check social media sites right after they wake up.
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