Answer:
Step-by-step explanation:
From the given information,
The required correct answers are,
1. The sample is:
b) simple random sample
2. np0 (1-p0) ___ 10
a) greater than or equal to
3. n ___ 0.05N
b) less than or equal to
Hypotheses:
4. H0:p___0.75
d) =
5. H1:p___0.75
a) ≠
6. The test statistic is a
a) z test statistic
7. test statistic=2.8284
8. p-value=0.0047
Decision:
Because p-value less than Alpha=0.05, we reject null hypothesis.
Conclusion:
The data support the claim that the proportion has changed.
Answer:
Step-by-step 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,
p = 3/4 = 0.75
For the alternative hypothesis,
p ≠ 0.75
Considering the population proportion, probability of success, p = 0.75
q = probability of failure = 1 - p
q = 1 - 0.75 = 0.25
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 480
n = number of samples = 600
P = 480/600 = 0.8
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.8 - 0.75)/√(0.75 × 0.25)/480 = 2.53
Recall, population proportion, P = 0.75
The difference between sample proportion and population proportion(P - p) is 0.8 - 0.75 = 0.05
Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.75 - 0.05 = 0.7
the p for the right tail is 0.75 + 0.05 = 0.8
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 above the test z score in the right tail 1 - 0.9943 = 0.0057
We would double this area to include the area in the left tail of z = - 2.53. Thus
p = 0.0057 × 2 = 0.0114
Because alpha, 0.05 > than the p value, 0.0114, then we would reject the null hypothesis.
Therefore, at 5% significance level, this data provide evidence that the proportion has changed.
