11 What is the purpose of calculating a confidence interval

11- What is the purpose of calculating a confidence interval?

To provide a range of values that has a certain large probability of containing the sample statistic of interest

To provide a range of values that, with a certain measure of confidence, contains the sample statistic of interest

To provide a range of values that, with a certain measure of confidence, contains the population parameter of interest

To provide a range of values that has a certain large probability of containing the population parameter of interest

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12-What is the most typical form of a calculated confidence interval?

Point estimate ± Standard error

Point estimate ± Margin of error

Population parameter ± Standard error

Population parameter ± Margin of error

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13- We draw a random sample of size 25 from the normal population with the variance 2.4. If the sample mean is 12.5, what is a 99% confidence interval for the population mean?

[11.2600, 13.7400]

[11.3835, 13.6165]

[11.7019, 13.2981]

[11.7793, 13.2207]

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14- The daily revenue from the sale of fried dough at a local street vendor in Boston is known to be normally distributed with a known standard deviation of $120. The revenue on each of the last 25 days is noted, and the average is computed as $550. A 95% confidence interval is constructed for the population mean revenue. If the data from the last 40 days had been used, then the resulting 95% confidence intervals would have been _____________________.

Wider, with a larger probability of reporting an incorrect interval

Wider, with the same probability of reporting an incorrect interval

Narrower, with a larger probability of reporting an incorrect interval

Narrower, with the same probability of reporting an incorrect interval

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15- Construct a 99% confidence interval on the population proportion for the support of candidate A in the following mayoral election. Candidate A is facing two opposing candidates. In a recent poll of 300 residents, 98 supported candidate B and 58 supported candidate C.

[0.4057, 0.5543]

[0.4130, 0.5470]

[0.4779, 0.4821]

[0.4781, 0.4819]

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16- In general, the null and alternative hypotheses are __________.

Additive

Correlated

Multiplicative

Mutually exclusive

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17- It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies that are born out of wedlock is increasing. Identify the correct null and alternative hypotheses to test the politician’s claim.

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18- For a given sample size , ________________.

Decreasing the probability of a Type I error will increase the probability of a Type II error

Decreasing the probability of a Type I error will decrease the probability of a Type II error

Changing the probability of a Type I error will have no impact on the probability of a Type II error

Increasing the probability of a Type I error will increase the probability of a Type II error as long as is known

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19- A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. The value of the test statistic is ____________.

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20-A school teacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L. The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L. At a 5% significance level, the critical value(s) is (are) _______.

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Solution

Q11.
To provide a range of values that, with a certain measure of confidence, contains the population parameter of interest

With the confidence calculated we measure the level of true population mean

Q12.
Point estimate ± Margin of error
Confidence Interval

CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Margin of error = t a/2 * (sd/ Sqrt(n))