# Get help with statistics and probability

Recent questions in Statistics and Probability
Study design

### 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 $$\begin{array}{cc} 15&14&14&14&3&12&11&11&11&11&10&11&13&16&10\\ 9&15&12&9&10&7&14&13&14&8&9&8&11&13&13 \\ 15&12&9&10&9&9&16&16&12&10&11&11&12&15&8\\ 10&10&10&11&9 \end{array}$$ (a) Make a box-and-whisker plot of the data. Find the interquartile range.

Sampling distributions

### Resource managers of forest game lands were concerned about the size of the deer and rabbit populations during the winter months in a particular forest. As an estimate of population size, they proposed using the average number of pellet groups for rabbits and deer per 30-foot-square plots. From an aerial photograph, the forest was divided into N= 10,000 30-foot-square grids. A simple random sample of 2 = 500 plots was taken, and the number of pellet groups was observed for rabbits and for deer. The results of this study are summarized in the accompanying table. a. Estimate $$\displaystyle\mu_{{1}},{\quad\text{and}\quad}\mu_{{2}}$$, the average number of pellet groups for deer and rabbits, respectively, per 30-foot-square-plots. Place bounds on the errors of estimation. b. Estimate the difference in the mean size of pellet groups per plot for the two animals, with an appropriate margin of error. Deer Sample mean = 2.30 Sample variance = 0.65 Rabbits Sample mean = 4.52 Sample variance = 0.97

Confidence intervals

Random variables

Random variables

Two-way tables

Two-way tables

### The two-way table summarizes information about eye color and gender in a random sample of 200 high school students.

Confidence intervals

Two-way tables

Two-way tables

Two-way tables

Study design

### State whether the investigation in question is an observational study or a designed experiment. Justify your answer in each case.In the 1940s and early 1950s, the public was greatly concerned about polio. In an attempt to prevent this disease, Jonas Salk of the University of Pittsburgh developed a polio vaccine. In a test of the vaccine’s efficacy, involving nearly 2 million grade-school children, half of the children received the Salk vaccine. the other half received a placebo, in this case an injection of salt dissolved in water. Neither the children nor the doctors performing the diagnoses knew which children belonged to which group, but an evaluation center did. The center found that the incidence of polio was far less among the children inoculated with the Salk vaccine. From that information, the researchers concluded that the vaccine would be effective in preventing polio for all U.S. school children. consequently, it was made available for general use.

Summarizing quantitative data

### Refer to the Journal of Applied Psychology (Jan. 2011) study of the determinants of task performance. In addition to x1 = conscientiousness score and x2 = {1 if highly complex job, 0 if not}, the researchers also used x3 = emotional stability score, x4 = organizational citizenship behavior score, and x5 = counterproductive work behavior score to model y = task performance score. One of their concerns is the level of multicollinearity in the data. A matrix of correlations for all possible pairs of independent variables follows. Based on this information, do you detect a moderate or high level of multicollinearity? If so, what are your recommendations? x1 x2 x3 x4 Conscientiousness (x1) Job Complexity (x2).13 Emotional Stability (x3).62.14 Organizational Citizenship (x4).24.03.24 Counterproductive Work (x5)-.23-.23-.02-.62

Confidence intervals

Two-way tables

Two-way tables

### Is there a relationship between gender and relative finger length? To investigate, a random sample of 452 U.S. high school students was selected. The two-way table shows the gender of each student and which finger was longer on his or her left hand (index finger or ring finger). State the hypotheses for a test of the relationship between gender and relative finger length for U.S. high school students. $$\begin{array}{|l|c|r|c|} \hline & \text { Female } & \text { Male } & \text { Total } \\ \hline \text { Index finger } & 78 & 45 & 123 \\ \hline \text { Ring finger } & 82 & 152 & 234 \\ \hline \text { Same length } & 52 & 43 & 95 \\ \hline \text { Total } & 212 & 240 & 452 \\ \hline \end{array}$$

Comparing two groups

### Water flows through a water hose at a rate of $$\displaystyle{Q}_{{{1}}}={680}{c}\frac{{m}^{{{3}}}}{{s}}$$, the diameter of the hose is $$\displaystyle{d}_{{{1}}}={2.2}{c}{m}$$. A nozzle is attached to the water hose. The water leaves the nozzle at a velocity of $$\displaystyle{v}_{{{2}}}={9.2}\frac{{m}}{{s}}$$. a) Enter an expression for the cross-sectional area of the hose, $$\displaystyle{A}_{{{1}}}$$, in terms of its diameter, $$\displaystyle{d}_{{{1}}}$$ b) Calculate the numerical value of $$\displaystyle{A}_{{{1}}},$$ in square centimeters. c) Enter an expression for the speed of the water in the hose, $$\displaystyle{v}_{{{1}}}$$, in terms of the volume floe rate $$\displaystyle{Q}_{{{1}}}$$ and cross-sectional area $$\displaystyle{A}_{{{1}}}$$ d) Calculate the speed of the water in the hose, $$\displaystyle{v}_{{{1}}}$$ in meters per second. e) Enter an expression for the cross-sectional area of the nozzle, $$\displaystyle{A}_{{{2}}}$$, in terms of $$\displaystyle{v}_{{{1}}},{v}_{{{2}}}$$ and $$\displaystyle{A}_{{{1}}}$$ f) Calculate the cross-sectional area of the nozzle, $$\displaystyle{A}_{{{2}}}$$ in square centimeters.

Confidence intervals

### In a science fair​ project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left​ hand, and then she asked the therapists to identify the selected hand by placing their hand just under​ Emily's hand without seeing it and without touching it. Among 358 ​trials, the touch therapists were correct 172 times. Complete parts​ (a) through​ (d). a) Given that Emily used a coin toss to select either her right hand or her left​ hand, what proportion of correct responses would be expected if the touch therapists made random​ guesses? ​(Type an integer or a decimal. Do not​ round.) b) Using​ Emily's sample​ results, what is the best point estimate of the​ therapists' success​ rate? ​(Round to three decimal places as​ needed.) c) Using​ Emily's sample​ results, construct a $$\displaystyle{90}​\%$$ confidence interval estimate of the proportion of correct responses made by touch therapists. Round to three decimal places as​ needed - ?$$\displaystyle{<}{p}{<}$$?

Upper level probability