Chp 8 QUIZ STA 2023 McGraw Hill

Suppose we wish to find the required sample size to find a 90% confidence interval for the population proportion with the desired margin of error. If there is no rough estimate formula259.mml of the population proportion, what value should be assumed for formula259.mml?

0.50 For a desired margin of error E, the minimum sample size n required to estimate a formula256.mml confidence interval for the population proportion is computed as formula257.mml is a reasonable estimate of formula258.mml in the planning stage. Use z table.

Which of the following is the necessary condition for creating confidence intervals for the population mean?

Normality of the estimator For the confidence interval, the estimator formula55.mml must be at least approximately normally distributed. By the central limit theorem, even when the population is not normally distributed, this condition is satisfied as long as the sample size 1formula56.mml

If a random sample of size n is taken from a normal population with a finite variance, then the statisticformula20.mmlfollows the tdf distribution with (n −1) degrees of freedom, df.

True If a random sample of size n is taken from a normal population with a finite variance, then the statisticformula21.mmlfollows the tdf distribution with (n −1) degrees of freedom, df.

The minimum sample size n required to estimate a population mean with 95% confidence and the desired margin of error 1.5 was found to be 198. Which of the following is the approximate value of the assumed estimate of the population standard deviation?

10.7688 For a desired margin of error E, the minimum sample size n required to estimate a 1formula226.mml confidence interval for the population mean is computed as 1formula227.mml 1formula228.mml is a reasonable estimate of 1formula229.mml in the planning stage. Because the required sample size is rounded up the following is correct: 1formula230.mml . It can be derived that 1formula231.mml Use z table.

A politician wants to estimate the percentage of people who like his new slogan. Given that no prior estimate of the population proportion is available, what is the minimum sample size such that the margin of error is no more than 0.08 for a 95% confidence interval?

151 For a desired margin of error E, the minimum sample size n required to estimate a formula276.mml confidence interval for the population proportion is computed as formula277.mml is a reasonable estimate of formula278.mml in the planning stage. Use z table.

The GPA of accounting students in a university is known to be normally distributed. A random sample of 20 accounting students results in a mean of 2.92 and a standard deviation of 0.16. Construct the 95% confidence interval for the mean GPA of all accounting students at this university.

2.92 + 2.093 (0.16/sqrt(20)) Because the population standard deviation is unknown use tdf distribution. The confidence interval of the population mean is computed as formula100.mml. Use t table.

Statisticians like precision in their interval estimates. A low margin of error is needed to achieve this. Which of the following supports this when selecting sample sizes?

A larger sample size reduces the margin of error. If we are able to increase the size of the sample, the larger nreduces the margin of error for the interval estimates.

A confidence interval provides a value that, with a certain measure of confidence, is the population parameter of interest.

False A confidence interval provides a range of values that, with a certain level of confidence, contains the population parameter of interest.

For a given confidence levelformula5.mmland sample size n, the width of the confidence interval for the population mean is narrower, the greater the population standard deviation σ.

False For a given confidence levelformula6.mmland sample size n, the width of the confidence interval for the population mean is wider, the greater the population standard deviation σ.

The t distribution table lists tdf values for selected lower-tail probabilities and degrees of freedom df.

False The t distribution table lists tdf values for selected upper-tail probabilities and degrees of freedom df.

The tdf distribution consists of a family of distributions where the actual shape of each one depends on the degrees of freedom, df. For lower values of df, the tdf distribution is similar to the z distribution.

False The tdf distribution consists of a family of distributions where the actual shape of each one depends on the degrees of freedom, df. As df increases, the tdf distribution becomes more similar to the z distribution; it is identical to the z distribution when df is infinity.

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

Point estimate ± Margin of error It is common to construct a confidence interval as Point estimate ± Margin of error.

When the required sample size calculated by using a formula is not a whole number, what is the best choice for the required sample size?

Round the result of the calculation up to the nearest whole number. To be conservative, always round up noninteger values of the calculated required sample size.

When examining the possible outcome of an election, what type of confidence interval is most suitable for estimating the current support for a candidate?

The confidence interval for the population proportion Sometimes the parameter of interest describes a population that is qualitative rather than quantitative. The population proportion is the essential descriptive measure of when the data type is qualitative.

How do the tdf and z distributions differ?

The tdf distribution has broader tails (it is flatter around zero). The tdf distribution has broader tails than the z distribution.

The tdf distribution has broader tails than the z distribution.

True The tdf distribution has slightly broader tails than the z distribution.

In an examination of holiday spending (known to be normally distributed) of a sample of 16 holiday shoppers at a local mall, an average of $54 was spent per hour of shopping. Based on the current sample, the standard deviation is equal to $21. Find a 90% confidence interval for the population mean level of spending per hour.

[$44.7967, $63.2033] Because the population standard deviation is unknown use tdf distribution. The confidence interval of the population mean is computed as formula116.mml. Use t table.

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

[11.7019, 13.2981] The confidence interval for the population mean is computed as formula69.mml. Use z table.