QNT 2020 Exam 1

The figure shows a standard normal N(0,1) distribution. Find the z value for the shaded area. u=0 o=1 z=?? shaded area=0.04

-1.75 Explanation: Appendix C.2 gives P(z < − 1.75) = 0.0401 or use Excel = NORM.S.INV(0.04) = −1.75.

For a given sample size, when we increase the probability of a Type I error, the probability of a Type II error -remains unchanged. -decreases. -increases. -is impossible to determine without more information.

-Decreases Explanation: For a given sample size, there is a trade-off between α and β.

Simple regression analysis means that -the data are presented in a simple and clear way. -we have only one explanatory variable. -there are only two independent variables. -we have only a few observations.

-We only have one explanatory variable Explanation: Multiple regression has more than one independent variable (predictor).

Consider the following linear trend equation of an industry's sales: yt = 120 + 12 xt, where t is the time index (t = 1, 2, . . . , n) and yt is annual sales (in millions of dollars). Which is the most reasonable conclusion? -On the average, sales will increase 12/(120 + 12 ×10) = 0.05, or 5 percent next year. -We would forecast that sales will increase $12 million in the next year. -The year-to-year average change will depend on the value of t. -We would forecast that sales will increase 12 percent in the next year.

-We would forecast that sales will increase $12 million in the next year. Explanation: The slope is 12. Sales are in millions, so 12 represents $12 million.

Which statement about α is not correct? -It is the probability of committing a Type I error. -It is the test's significance level. -It is the probability of rejecting a true H0. -It is equal to 1 − β.

-its is equal to 1 − β. Explanation: There is an inverse relationship between α and β, but it is not a simple equation.

If the random variable Z has a standard normal distribution, then P(Z ≤ −1.72) is:

0.0427 Explanation: Use Appendix C or Excel = NORM.S.DIST(−1.72,1).

The figure shows a standard normal N(0,1) distribution. Find the shaded area. u=0 o=1 z=+0.44

0.3300 Explanation: Appendix C.2. gives 1 − P( z < 0.44) = 1 − 0.6700 = 0.3300 = 1 − NORM.S.DIST(0.44,1).

If adult male heights are normally distributed with a mean of 180 cm and a standard deviation of 7 cm, how high should an aircraft lavatory door be to ensure that 99.9 percent of adult males will not have to stoop as they enter?

201.6cm Explanation: With Excel, we get = NORM.INV(0.999,180,7) = 201.63, or Appendix C with z = 3.0

A population consists of the following data: 7, 11, 12, 18, 20, 22, 25. The population variance is:

36.82 Explanation: Use the population formula or Excel's =VAR.P(Data).

If the attendance at a baseball game is to be predicted by the equation Attendance = 16,500 − 75 Temperature, what would be the predicted attendance if Temperature is 90 degrees?

9750 Explanation: The predicted Attendance is 16,500 − 75(90) = 9,750.

Which probability model is most appropriate to describe the waiting time (working days) until an office photocopier breaks down (i.e., requires unscheduled maintenance)?

Exponential Explanation: Poisson breakdowns suggest exponential waiting time.

Chebyshev's Theorem says that at most 50 percent of the data lie within 2 standard deviations of the mean. True/False

False Explanation: At least 75 percent by Chebyshev.

A 90 percent confidence interval will be wider than a 95 percent confidence interval, ceteris paribus. True/False

False Explanation: For example, z0.025 = 1.960 (for 95 percent confidence) gives a wider interval than z0.05 = 1.645 (for 90 percent confidence). The proffered statement would also hold true for the Student's t distribution.

Outliers are data values that fall beyond ±2 standard deviations from the mean. True/False

False Explanation: Outliers are 3 standard deviations from the mean

The level of significance refers to the probability of making a Type II error. True/False

False Explanation: The level of significance is the desired probability of Type I error.

A higher confidence level leads to a narrower confidence interval, ceteris paribus. True/False

False Explanation: Higher confidence requires more uncertainty (a wider interval). For example, z0.025 = 1.960 (for 95 percent confidence) gives a wider interval than z0.05 = 1.645 (for 90 percent confidence). The proffered statement would also hold true for the Student's t distribution.

Could this function be a PDF?

No Explanation: Area = base × height = 2, which is not 1, so it cannot be a PDF.

If the mean and median of a population are the same, then its distribution is:

Symmetric Explanation: Any population is symmetric if its mean and median are equal. While the normal and uniform distributions are symmetric, there are other symmetric populations.

So far this year, stock A has had a mean price of $6.58 per share with a standard deviation of $1.88, while stock B has had a mean price of $10.57 per share with a standard deviation of $3.02. Which stock is more volatile?

They are the same Explanation: They are the same: CVA = 100(1.88/6.58) = 28.57%. CVB = 100(3.02/10.57) = 28.57%.

The correlation coefficient r measures the strength of the linear relationship between two variables. True/False

True Explanation: A correlation coefficient measures linearity between two variables.

The least squares regression line is obtained when the sum of the squared residuals is minimized. True/False

True Explanation: The Ordinary Least Squares (OLS) method minimizes the sum of squared residuals.

The efficiency of an estimator depends on the variance of the estimator's sampling distribution. True/False

True Explanation: Efficiency is measured by the variance of the estimator's sampling distribution.

In a simple regression, the correlation coefficient r is the square root of R2. True/False

True Explanation: In fact, we could use the notation r2 instead of R2 when talking about simple regression.

The Empirical Rule assumes that the distribution of data follows a normal curve. True/False

True Explanation: Unlike Chebyshev, the Empirical Rule assumes a normal population.

If R2 = .36 in the model Sales = 268 + 7.37 Ads, then Ads explains 36 percent of the variation in Sales. True/False

True Explanation: We interpret R2 as the fraction of variation in Y explained by X (expressed as a percentage).

When the sample standard deviation is used to construct a confidence interval for the mean, we would use the Student's t distribution instead of the normal distribution. True/False

True Explanation: We should use the t distribution when the population variance is unknown.

In constructing a confidence interval for the mean, the z distribution provides a result nearly identical to the t distribution when n is large. True/False

True Explanation: Student's t approaches z as the sample size increases.

Scatter plots are used to visualize association in samples of paired data (X, Y). True/False

True Explanation: That is exactly what a scatter plot is for.

A sample of size 5 shows a mean of 45.2 and a sample standard deviation of 6.4. The standard error of the sample mean is approximately 2.86.

True Explanation: The standard error is the standard deviation divided by the square root of the sample size. We would use Student's t instead of z to construct a confidence interval for the population mean, but this problem did not ask for a confidence interval.

A frequency distribution is a tabulation of n data values into classes called bins. True/False

True Explanation: This is the definition of a frequency distribution.