Answer: The alternative hypothesis represents the claim
Explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
µ = 0.38
For the alternative hypothesis,
µ > 0.38
Considering the population proportion, probability of success, p = 0.38
q = probability of failure = 1 - p
q = 1 - 0.38 = 0.6
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 176
n = number of samples = 400
P = 176/400 = 0.44
We would the test statistic which is the z score
z = (p - P)/√pq/n
z = (0.44 - 0.38)/√(0.38 × 0.62)/400 = 2.47
Recall, population proportion, P = 0.38
The difference between sample proportion and population proportion(P - p) is 0.44 - 0.38 = 0.06
Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.38 - 0.06 = 0.32
the p for the right tail is 0.38 + 0.06 = 0.44
These proportions are higher and lower 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 above z is 1 - 0.9932 = 0.0068
We would double this area to include the area in the left tail of z = - 2.47. Thus
p = 0.0068 × 2 = 0.014
Since alpha, 0.01 < than the p value, 0.014, then we would fail to reject the null hypothesis. Therefore, at a 1% level of significance, we do not have enough evidence to reject the null hypothesis