STA 296 Final Exam / Questions & Expertly Verified Answers, 2025 / 2026.
Qs: Consider random samples of size 55 from a population with proportion
0.35 . Find the standard error of the distribution of sample proportions. -
Answer:
Standard Error= 0.064
Qs: Consider random samples of size 120 from a population with proportion
0.51 . Find the standard error of the distribution of sample proportions.Round your answer for the standard error to three decimal places. -
Answer:
Standard Error= 0.046
Qs: Compute the standard error for sample proportions from a population
with proportion p = 0.25 for sample sizes of n = 40, n = 200, and n = 1200. -
Answer:
n=40: 0.0685
n=200: 0.031
n=1200: 0.013
Qs: What happens if the sample size goes up? -
Answer:
The standard error goes down
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Qs: What happens if the standard error goes down? -
Answer:
The sample proportions are less spread out from the population proportion, so the accuracy is better.
Qs: Is the sample size large enough so that the sample proportions follow a
normal distribution?n=400 and p=0.1 -
Answer:
yes
Qs: is the sample size large enough so that the sample proportions follow a
normal distribution?n=35 p=0.4 -
Answer:
yes
Qs: is the sample size large enough so that the sample proportions follow a
normal distribution?n=40 p=0.25 -
Answer:
yes
Qs: is the sample size large enough so that the sample proportions follow a
normal distribution?n=100
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p=0.95 -
Answer:
no
Qs: Use the normal distribution to find a confidence interval for a proportion
p given the relevant sample results.Give the best point estimate for p, the margin of error, and the confidence interval. Assume the results come from a random sample.A 90% confidence interval for p given that p^=0.41 and n=450.Round your answer for the best point estimate to two decimal places, and your answers for the margin of error and the confidence interval to three decimal places. -
Answer:
best estimate for p =0.41 the margin of error=±0.038 90% confidence interval for p= 0.372 to 0.448
Qs: Use the normal distribution to find a confidence interval for a proportion
p given the relevant sample results. Give the best point estimate for p, the margin of error, and the confidence interval. Assume the results come from a random sample.A 95% confidence interval for p given that p^=0.9 and n=130.Round your answer for the point estimate to two decimal places, and your answers for the margin of error and the confidence interval to three decimal places. -
Answer:
best estimate for p=0.9 the margin of error= ±0.052 the 95% confidence interval for p= 0.848 to 0.952 .
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Qs: Use the normal distribution to find a confidence interval for a proportion
p given the relevant sample results. Give the best point estimate for p, the margin of error, and the confidence interval. Assume the results come from a random sample.A 95% confidence interval for the proportion who will answer ''Yes" to a question, given that 67 answered yes in a random sample of 85 people.Round your answers to three decimal places. -
Answer:
best estimate for the proportion who will answer yes= 0.788 the margin of error= ±0.087 the 95% confidence interval for the proportion who will answer yes= 0.701 to 0.875 **Note that the margin of error is quite large since the sample size is relatively small.
Qs: What sample size is needed to give a margin of error within ±4% in
estimating a population proportion with 95% confidence? -
Answer:
sample size= 601
Qs: What sample size is needed to give a margin of error within ±2.5% in
estimating a population proportion with 99% confidence? -
Answer:
sample size= 1991
Qs: Find a 90% confidence interval for the proportion of household cats in the
US that hunt outdoors -
Answer:
The 90% confidence interval= 0.284 to 0.416
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