Note: if the population standard deviations o1 and oz, then we use the standard normal distribution.

Question

asked 2021-06-04

Consider the two samples of data from the McKenzie School. The numbers represent the time in seconds that it took each child to cover a distance of 50 meters. Girls’ Times: 8.3, 8.6, 9.5, 9.5, 9.6, 9.8, 9.9, 9.9, 10.0, 10.0, 10.0, 10.1, 10.3, 10.5 Boys’ Times: 7.9, 8.0, 8.2, 8.2, 8.4, 8.6, 8.8, 9.1, 9.3, 9.5, 9.8, 9.8, 10.0, 10.1, 10.3. Based on the sample means, do you conclude that the distributions of times from the boys’ population and girls’ population are different? Explain.

asked 2021-06-15

In government data, a house-hold consists of all occupants of a dwelling unit, while a family consists of 2 or more persons who live together and are related by blood or marriage. So all families form households, but some households are not families. Here are the distributions of household size and family size in the United States.

\(\text{Number of people}\\ \begin{array}{|l|c|c|c|c|c|c|c|} \hline & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \begin{array}{l} \text { Household } \\ \text { probability } \end{array} & 0.25 & 0.32 & 0.17 & 0.15 & 0.07 & 0.03 & 0.01 \\ \hline \begin{array}{l} \text { Family } \\ \text { probability } \end{array} & 0 & 0.42 & 0.23 & 0.21 & 0.09 & 0.03 & 0.02 \\ \hline \end{array}\)

Let H = the number of people in a randomly selected U.S. household and F = the number of people in a randomly chosen U.S. family. The standard deviations of the 2 random variables are \(\sigma H=1.421\) and \(\sigma F=1.249.\) Explain why this difference makes sense.

asked 2021-06-23

The pathogen Phytophthora capsici causes bell pepper plants to wilt and die. A research project was designed to study the effect of soil water content and the spread of the disease in fields of bell peppers. It is thought that too much water helps spread the disease. The fields were divided into rows and quadrants. The soil water content (percent of water by volume of soil) was determined for each plot. An important first step in such a research project is to give a statistical description of the data.
Soil Water Content for Bell Pepper Study
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(a) Make a box-and-whisker plot of the data. Find the interquartile range.

asked 2021-06-03

In government data, a household consists of all occupants of a dwelling unit, while a family consists of 2 or more persons who live together and are related by blood or marriage. So all families form households, but some households are not families. Here are the distributions of household size and family size in the United States. \(\text{Number of people}\ \begin{array}{|l|c|c|c|c|c|c|c|} \hline & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \begin{array}{l} \text { Household } \\ \text { probability } \end{array} & 0.25 & 0.32 & 0.17 & 0.15 & 0.07 & 0.03 & 0.01 \\ \hline \begin{array}{l} \text { Family } \\ \text { probability } \end{array} & 0 & 0.42 & 0.23 & 0.21 & 0.09 & 0.03 & 0.02 \\ \hline \end{array}\)

Let \(H =\) the number of people in a randomly selected U.S. household and \(F =\) the number of people in a randomly chosen U.S. family. Find the expected value of each random variable. Explain why this difference makes sense.