Answer:
Step-by-step explanation:
a) We would set up the hypothesis test.
For the null hypothesis,
p = 0.25
For the alternative hypothesis,
p ≠ 0.25
b) The test statistic to be used is the z test. The formula is
z = (P - p)/√pq/n
c) Considering the population proportion, probability of success, p = 0.25
q = probability of failure = 1 - p
q = 1 - 0.25 = 0.75
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 141
n = number of samples = 600
P = 141/600 = 0.235
Therefore
z = (0.235 - 0.25)/√(0.25 × 0.75)/600 = - 0.85
d) Recall, population proportion, p = 0.25
The difference between sample proportion and population proportion is 0.25 - 0235. = 0.015
Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.25 - 0.015 = 0.235
the p for the right tail is 0.25 + 0.015 = 0.265
These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area
From the normal distribution table, the area below the test z score in the left tail 0.198
We would double this area to include the area in the right tail of z = 0.85. Thus
p = 0.198 × 2 = 0.396
e) Since alpha, 0.01 < than the p value, 0.396, then we would fail to reject the null hypothesis.
f) In a sample of 600 cars, we would observe a sample proportion of 0.015 or more away from 0.25 about 39.6% of the time by chance alone. Therefore, the sample result is not statistically significant because it could occur in 39.6% of the time by chance alone.
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(Where k is constant of proportionality).....(3)
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