Question

The given data set consists of two sets of sample observations:

First set:
3.86, 4.92, 4.15, 4.36, 4.09, 4.30, 4.66, 4.40, 4.45, 4.42

Second set:
3.83, 4.34, 4.56, 4.24, 4.33, 4.23, 4.28, 4.63, 4.34, 3.73

Which one of the following statements is true regarding the first set of data?

(A) The ratio of IQR to standard deviation suggests that the observations are from a normal population.
(B) The normal probability plot suggests that the observations are not distributed normally (i.e., in a bell-shaped).
(C) The stemplot with ones and tenths as stems and hundredths as leaves suggests that the observations are not distributed normally (i.e., in a bell-shaped).
(D) According to standard scores, the data set contains at least one outlier.
(E) According to quartiles, the data set contains one outlier.
(F) According to the boxplot, the observations are heavily skewed to the left.
(G) The ratio of IQR to standard deviation suggests that the observations are not from a normal population.
(H) None.

Answer 1

To decide whether any of the given statements about the first data set are true, we must perform statistical calculations on IQR, standard deviation, and potential outliers, and visually assess normality and skewness. Without specific numerical values and visual plots, we cannot confirm any of the provided statements.

Step-by-step explanation:

To determine which statement is true regarding the first set of data, we must analyze key statistical properties like the interquartile range (IQR), standard deviation, and potential outliers using established criteria.

• IQR: We would calculate IQR by finding the difference between the third quartile (Q3) and the first quartile (Q1).
• Outliers: To find outliers, we would typically use the IQR and consider any values less than Q1 - 1.5(IQR) or greater than Q3 + 1.5(IQR) as potential outliers.
• Standard Deviation: This measures the spread of a data set and plays a role in understanding the distribution.

Without the actual calculations for the standard deviation and IQR, statements like A and G cannot be confirmed. For outliers, we would need to know the specific quartiles' values and perform calculations to identify if any exist in either set, dismissing choice D and E without that information. More importantly, though, the normality of a distribution is often assessed through a normal probability plot, and its shape can be visualized using a stemplot or boxplot for skewness. Based on the information given, the shape of the distribution and skewness cannot be ascertained, so choices B, C, and F cannot be verified.

Answer 2

To accurately verify the statement regarding the ratio of IQR to standard deviation and its implication for the normality of the data set, we need to perform calculations on the IQR and standard deviation. These measures are critically important in assessing the spread and distribution of the data in order to make any interpretations.

Step-by-step explanation:

When considering the statements regarding the first set of sample observations, it is necessary to calculate and compare statistical measures such as the interquartile range (IQR) and standard deviation. The IQR is the range of the middle 50 percent of the data, calculated by subtracting the first quartile (Q1) from the third quartile (Q3). The standard deviation measures how spread out the numbers are in the data set.

To determine whether the statement about the ratio of IQR to standard deviation suggesting that the observations are not from a normal population is true, specific calculations are needed:

• Calculate the IQR for the first set.
• Calculate the standard deviation for the first set.
• Compare the ratio of IQR to standard deviation.

Without the actual computations provided in the question, we cannot claim the truth of any given statement definitively. However, statement (G) which mentions the ratio of IQR to standard deviation suggesting a non-normal population would require actual data analysis to verify. It is important to remember that the IQR and standard deviation are measures of spread, and interpreting them requires numerical computations and sometimes a graphical representation like a boxplot or histogram.