 # College Statistics & Probability Questions and Answers

Recent questions in College Statistics sagnuhh 2020-10-26 Answered

### Listed below are amounts of strontium-90 (in millibecquerels or mBq per gram of calclum) in a simple random sample of baby teth obtained from resident of state A and state B. Use a 0.05 significance level to test the celm that amounts of Strontium-90 from state A residents vary more than amounts from state B resints. Assume that both samples are independent simple random samples from populations having normal distributions. $\begin{array}{cccccccccccc}StateA:& 162& 143& 150& 130& 152& 152& 143& 155& 131& 139& 164\\ StateB:& 136& 140& 142& 131& 133& 129& 141& 140& 142& 136& 142\end{array}$ defazajx 2020-10-26 Answered

### A population of values has a normal distribution with $\mu =198.8$ and $\sigma =69.2$. You intend to draw a random sample of size $n=147$. Find the probability that a single randomly selected value is between 184 and 205.1. $P\left(184? Write your answers as numbers accurate to 4 decimal places. Nann 2020-10-25 Answered

### Is isomorpbic to ${Z}_{27}?$ Decide and answer why exactly? CheemnCatelvew 2020-10-25 Answered

### If $n=110$ and $\stackrel{^}{p}$ (p-hat) $=0.66$, construct a $95\mathrm{%}$ confidence interval. Give your answers to two decimals $? cistG 2020-10-25 Answered

### A normal population has mean $\mu =20$ and standard deviation $\sigma =4$. What proportion of the population is less than 18? Efan Halliday 2020-10-25 Answered

### A population of values has a normal distribution with $\mu =120.6$ and $\sigma =48.5$. You intend to draw a random sample of size $n=105$. Find the probability that a sample of size $n=105$ is randomly selected with a mean greater than 114.9. $P\left(M>114.9\right)=$? Write your answers as numbers accurate to 4 decimal places. Globokim8 2020-10-25 Answered

### A population of values has a normal distribution with $\mu =239.5$ and $\sigma =32.7$. You intend to draw a random sample of size $n=139$. Find the probability that a sample of size $n=139$ is randomly selected with a mean greater than 235.9. $P\left(M>235.9\right)=$? Write your answers as numbers accurate to 4 decimal places. facas9 2020-10-23 Answered

### A population of values has a normal distribution with $\mu =116.3$ and $\sigma =27.5$. You intend to draw a random sample of size $n=249$. Find the probability that a single randomly selected value is greater than 117.3. $P\left(X>117.3\right)=$? Write your answers as numbers accurate to 4 decimal places. Jaya Legge 2020-10-23 Answered

### Researchers wanted to compare the effectiveness of a water softener used with a filtering process with a water softener used without filtering. Ninety locations were randomly divided into two groups of equal size. Group A locations used a water softener and the filtering process, while group B used only the water softener. At the end of three months, a water sample was tested at each location for its level of softness. (Water softness was measured on a scale of 1 to 5, with 5 being the softest water.) The results were as follows: Group A (water softener and filtering) ${x}_{1}=2.1$ ${s}_{1}=0.7$ Group B (water softener only) ${x}_{2}=1.7$ ${s}_{2}=0.4$ Determine, at the 90% confidence level, whether there is a difference between the two types of treatments. bobbie71G 2020-10-23 Answered

### Identify the variable being measured. postillan4 2020-10-23 Answered

### Differentiate between univariate, bivariate and multivariate data. postillan4 2020-10-23 Answered

### A random sample of ${n}_{1}=16$ communities in western Kansas gave the following information for people under 25 years of age. ${X}_{1}:$ Rate of hay fever per 1000 population for people under 25 $\begin{array}{|cccccccc|}\hline 97& 91& 121& 129& 94& 123& 112& 93\\ 125& 95& 125& 117& 97& 122& 127& 88\\ \hline\end{array}$ A random sample of ${n}_{2}=14$ regions in western Kansas gave the following information for people over 50 years old. ${X}_{2}:$ Rate of hay fever per 1000 population for people over 50 $\begin{array}{|ccccccc|}\hline 94& 109& 99& 95& 113& 88& 110\\ 79& 115& 100& 89& 114& 85& 96\\ \hline\end{array}$ (i) Use a calculator to calculate ${\stackrel{―}{x}}_{1},{s}_{1},{\stackrel{―}{x}}_{2},\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}{s}_{2}.$ (Round your answers to two decimal places.) (ii) Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use $\alpha =0.05.$ (a) What is the level of significance? State the null and alternate hypotheses. ${H}_{0}:{\mu }_{1}={\mu }_{2},{H}_{1}:{\mu }_{1}<{\mu }_{2}$ ${H}_{0}:{\mu }_{1}={\mu }_{2},{H}_{1}:{\mu }_{1}>{\mu }_{2}$ ${H}_{0}:{\mu }_{1}={\mu }_{2},{H}_{1}:{\mu }_{1}\ne {\mu }_{2}$ ${H}_{0}:{\mu }_{1}>{\mu }_{2},{H}_{1}:{\mu }_{1}={\mu }_{12}$ (b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume that both population distributions are approximately normal with known standard deviations. The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations, The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations, The Student's t. We assume that both population distributions are approximately normal with known standard deviations, What is the value of the sample test statistic? (Test the difference ${\mu }_{1}-{\mu }_{2}$. Round your answer to three decimalplaces.) What is the value of the sample test statistic? (Test the difference ${\mu }_{1}-{\mu }_{2}$. Round your answer to three decimal places.) (c) Find (or estimate) the P-value. P-value $>0.250$ $0.125 $0,050 $0,025 $0,005 P-value $<0.005$ Sketch the sampling distribution and show the area corresponding to the P-value. P.vaiue Pevgiue P-value f P-value Jerold 2020-10-23 Answered FizeauV 2020-10-23 Answered

### 1. Find each of the requested values for a population with a mean of $?=40$, and a standard deviation of $?=8$ A. What is the z-score corresponding to $X=52?$ B. What is the X value corresponding to $z=-0.50?$ C. If all of the scores in the population are transformed into z-scores, what will be the values for the mean and standard deviation for the complete set of z-scores? D. What is the z-score corresponding to a sample mean of $M=42$ for a sample of $n=4$ scores? E. What is the z-scores corresponding to a sample mean of $M=42$ for a sample of $n=6$ scores? 2. True or false: a. All normal distributions are symmetrical b. All normal distributions have a mean of 1.0 c. All normal distributions have a standard deviation of 1.0 d. The total area under the curve of all normal distributions is equal to 1 3. Interpret the location, direction, and distance (near or far) of the following zscores: $a.-2.00b.1.25c.3.50d.-0.34$ 4. You are part of a trivia team and have tracked your team’s performance since you started playing, so you know that your scores are normally distributed with $\mu =78$ and $\sigma =12$. Recently, a new person joined the team, and you think the scores have gotten better. Use hypothesis testing to see if the average score has improved based on the following 8 weeks’ worth of score data: $82,74,62,68,79,94,90,81,80$. 5. You get hired as a server at a local restaurant, and the manager tells you that servers’ tips are $42 on average but vary about $12\left(\mu =42,\sigma =12\right)$. You decide to track your tips to see if you make a different amount, but because this is your first job as a server, you don’t know if you will make more or less in tips. After working 16 shifts, you find that your average nightly amount is$44.50 from tips. Test for a difference between this value and the population mean at the $\alpha =0.05$ level of significance. emancipezN 2020-10-21 Answered

### Identify which assumption is needed to use the linear regression model to make inferences about the relationship. Identify which assumption is the least critical. shadsiei 2020-10-21 Answered

### After hearing of the national result that 44% of students engage in binge drinking (5 dri a sitting for men, 4 for women), a professor surveyed a random sample of 244 students at his college and found that 96 of them admitted to binge drinking in the past week. Should he be surprised at this result? Explain. Tabansi 2020-10-21 Answered

### What does the variance of a random variable measure? What is the standard deviation of a continuous random variable X? mattgondek4 2020-10-21 Answered

### For each of the following test, outline a research scenario and use any hypothetical data to show how the test is conducted. Paired two-sample t-test boitshupoO 2020-10-21 Answered

### An in-ground pond has the shape of a rectangular prism. The pond has a depth of 24 inches and a volume of 72,000 cubic inches. The length of the pond is two times its width. Find the length and width of the pond. nitraiddQ 2020-10-21 Answered

### Explain which measure of spread would best describe the payroll:the range,the IQR, or the standard deviation.

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