Please answer, i don't know how to solve them. please and thank you
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Answer:
a) The sampling distribution for n=540 has a mean sample proportion of p=0.37 and a standard deviation of σs=0.0208.
b) probability = 0.99998
d) probability = 0.99874
e) You gain 0.12% in probability for an increase of 80% in sample size.
The increase in sample size is not justified by the increase in probability, for this margin of error (Δp=0.09).
Step-by-step explanation:
a) We have a known population proportion π=0.37 and we have to describe the sampling distribution when the sample size is n=540.
The mean sample proportion is expected to be the same as the population proportion:
The standard deviation of the sampling will be the population standard deviation divided by the square root of the sample size:
Then, we can say that the sampling distribution will have a p=0.37 and a standard deviation σs=0.0208.
b) We have to calculate the probability that the sample proportion will be within 0.09 of the population proportion.
We can calculate the z-value as:
As the distribution is symmetrical, we can calculate the probabilty that he sample proportion will be within 0.09 of the population proportion as:
probability = 0.99998
d. Now the sample is smaller (n=300), so the standard deviation of the samping distribution:
We have to recalculate the z-scores:
And the probability is:
probability = 0.99874
e. The increase in sample size is 80%
and the increase in probability is 0.12%
You gain 0.12% in probability for an increase of 80% in sample size.
The increase in sample size is not justified by the increase in probability, for this margin of error (Δp=0.09).
Looking at the image attached, we can see the assumed sales of the Chewy Candy Company for its new candy bar in Manila and Seoul. Setting up the given condition for separate branches, we clearly see that during the 6th month, the total sales in Manila first exceeded the cumulative total sales in Seoul.
