QUESTION 1 Regarding point estimates and confidence interval estimates, which on

Question

QUESTION 1

Regarding point estimates and confidence interval estimates, which one of the following statements is FALSE?

For both estimates we assume that the observations are independent.

An indication of the error due to sampling is only provided for a confidence interval estimate.

For both estimates we assume that the population distribution of the variable (X) is approximately Normal.

Both estimates are calculated using sample data

For both estimates, a larger sample size means a more precise estimate

QUESTION 2

Examine the following statements and then select the one statement that is correct.

A narrower confidence interval is always better than a wider confidence interval.

The width of a confidence interval is affected by both the sampling error and the required level of confidence.

For a 95% confidence interval for a population mean, there is a 95% chance that the confidence interval includes the sample mean.

A wider confidence interval means less confidence in the estimate (all other things being equal).

QUESTION 3

A 95% confidence interval was constructed for a population mean (sigma known). Suppose we are planning to repeat the study but we only have sufficient resources to take a sample that is one quarter the size of that used in the original study. Assuming we require the same level of confidence (and sigma has not changed), then the resulting margin of error (m.o.e.) for our new confidence interval will be:

4 times the original margin of error

twice the original margin of error

1/ 2 times the original margin of error

1/4 times the original margin of error

2 times the original margin of error

QUESTION 4

You want to compute a 90% confidence interval for the mean of a population with unknown standard deviation. The sample size is 30. The correct table value for calculating the required confidence interval is:-

1.96

1.6449

1.697

1.311

1.699

QUESTION 5

For confidence interval estimates, which of the following statements is FALSE

increasing the sample size decreases the width of the confidence interval

a 95% confidence interval for the mean (with population standard deviation known) will be narrower than a 99% confidence interval

the width of the confidence interval increases as we demand more confidence

using a sample standard deviation instead of the population standard deviation always results in a wider confidence interval

QUESTION 6

A 95% confidence interval for a population mean () was found to be (30.6, 42.8). Based on this information, a 0% confidence interval for ( ) would be: (state your answer correct to one decimal place) ___________

QUESTION 7

A simple random sample of seven (7) students is selected, and the students are asked how much time they spent studying for their University subjects (combined) outside class times. From past experience, it is known that these times (in hours) are distributed normally.

The times (in hours) for the sample of students are as follows:

Based on these results, a confidence interval estimate for the population mean is found to be 5.9 ± 2.6.

The level of confidence the researcher has used is closest to:-

90%

95%

99%

97.5%

  

QUESTION 8

A researcher wishes to construct a 95% confidence interval for a population mean. She selects a simple random sample of size 8 from the population. The population is normally distributed and is unknown. When constructing the confidence interval estimate, the researcher uses the table value from the normal distribution tables. The confidence level of her resulting confidence interval estimate will be

Less than 95% but greater than 90%.

Greater than 95%

Exactly 95%

Less than 90%

Exactly 90%

QUESTION 9

A 95% confidence interval for the proportion of sea fans infected on the Las Redes Reef was calculated to be (0.423, 0.615)

Based on this confidence interval, which one of the following statements is necessarily TRUE?

We don't know exactly what proportion of sea fans on the Las Redes Reef are infected but we know that it is definitely between 0.423 and 0.615.

We can be 95% certain that plausible values for the proportion of sea fans infected on the Las Redes Reef are between 0.423 and 0.615.

51.9% of all sea fans are infected.

If the study was repeated many times over, and the sample proportion of infected sea fans (p-hat) was recorded each time, then we would expect approximately 95% of the resulting estimates (the p_hat's) to be between (0.423 0.615).

51.9% of all sea fans on the Las Redes Reef are infected

QUESTION 10

Researchers are planning a study to estimate the proportion of students who use an iPad in lectures, rather than taking hand-written notes.

Take a sample of 1537 students.

Take a sample of 1200 students.

Take a sample of 2305 students, if you want to achieve that level of confidence and that margin of error.

Take a sample of 2401 students at the absolute minimum!

a.

For both estimates we assume that the observations are independent.

b.

An indication of the error due to sampling is only provided for a confidence interval estimate.

c.

For both estimates we assume that the population distribution of the variable (X) is approximately Normal.

d.

Both estimates are calculated using sample data

e.

For both estimates, a larger sample size means a more precise estimate

Explanation / Answer

Question 1

For both estimates we assume that the population distribution of the variable (X) is approximately Normal.

That means we have sone cases where we can find Confidence interval even if the population is not normal like chi-square, t-distribution.

Question 2

The width of a confidence interval is affected by both the sampling error and the required level of confidence.

As actually confidence interval based on standard error and significance level.

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