Here is Morgan's solution to this problem. 6,404 + 2,857 = 9,261 Which expression could Morgan use to check her work? A. 9,261 +
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Answer:
a) The probability is P=0.3982.
b) No. There is no enough evidence to say that the proportion of the population is not 0.6.
Step-by-step explanation:
a) In this question, we have a sample of the population, of size n=1000. To know what is the probability of observing a sample proportion that is at least 0.64 we have to know the parameters of the sampling distribution.
The parameters of the sampling distribution of the proportion will be:
With these parameters, we can calculate the z-value for p=0.64 as:
Then, we can calculate the probability of having a sample with p≥0.64:
b) To know if the proportion of the population is greater than 0.6 the rigth thing to do is perform a hypothesis test, in which we test the following hypothesis:
If the null hypothesis is rejected, we can conclude that there is evidence that the proportion of the population is greater than 0.6.
First, we assume a significance level of 0.05.
Second, we calculate the z value:
The P-value for this z is P=0.4. The P-value is greater than the significance level, what means that there is no evidence to reject the null hypothesis.
In other words, a sample mean of 0.64 is a quite probable value even if the proportion of the population is 0.6.