Answer:
Step-by-step explanation:
We would set up the hypothesis test.
For the null hypothesis,
P = 0.22
For the alternative hypothesis,
P < 0.22
This is a left tailed test
Considering the population proportion, probability of success, p = 0.22
q = probability of failure = 1 - p
q = 1 - 0.22 = 0.78
Considering the sample,
Sample proportion, p = x/n
Where
x = number of success = 230
n = number of samples = 1189
p = 230/1189 = 0.19
We would determine the test statistic which is the z score
z = (p - P)/√pq/n
z = (0.19 - 0.22)/√(0.22 × 0.78)/1189 = - 2.5
Recall, population proportion, p = 0.22
We want the area to the left of 0.22 since the alternative hypothesis is lesser than 0.22. Therefore, from the normal distribution table, the probability of getting a proportion < 0.22 is 0.00621
So p value = 0.00621
Since alpha, 0.01 > than the p value, 0.00621, then we would reject the null hypothesis.
Referring to the above, the null hypothesis will be rejected if the test statistic is - 2.5
,
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