 # College Statistics & Probability Questions and Answers

Recent questions in College Statistics vacinammo288 2022-04-30 Answered

### Provide a thorough response to the two following questions.1. What is hypothesis testing? Provide all basic components, including error types, with explanations.2.What is the difference between chi-square goodness of fit and chi-square test of independence? What do they have in common? Ari Sheppard 2022-04-29 Answered

### Let ${X}_{1},\dots {X}_{n}$ be iid . A $95\mathrm{%}$ confidence interval for $\theta$ is $\stackrel{―}{X}±\frac{1.96}{\sqrt{n}}$. Let p denote the probability that an additional independent observation, ${X}_{n+1}$, will fall in this interval. Is p greater than, less than, equal to $0.95$? Prove your answer. p3sa1bynn 2022-04-29 Answered

### Let ${x}_{1},\cdots ,{x}_{n}$ be a sample from a normal population having unknown mean and variance. Let $\stackrel{―}{x}$ be the average of the first n of them.What is the distribution of ${x}_{n+1}-\stackrel{―}{x}$?If $\stackrel{―}{x}=4$, give an interval that, with $90\mathrm{%}$ confidence, will contain the value of ${x}_{n+1}$.The distribution of $\stackrel{―}{x}$ would be normal with mean equal to the population mean and standard deviation equal to the population standard deviation divided by $\sqrt{n}$. But how do we find the distribution of ${x}_{n+1}$? dooporpplauttssg 2022-04-29 Answered

### Let ${X}_{1},\cdots ,{X}_{n}$ be a random sample from $f\left(x\mid \theta \right)=\theta {x}^{\theta -1}$ for $0. Find a confidence interval for $\theta$ using as pivotal quantity a function of the maximum likelihood estimator for $\theta$. Terrence Moore 2022-04-29 Answered

### Let K be the number of heads in 200 flips of a coin. The null hypothesis H is that the coin is fair. Devise significance tests with the folowng properties.Note: Your answers below must be integersa) The signficance level is $\alpha$ =0.08 and the rejection set R has the form $\left\{|K-E\left[K\right]|>c\right\}.$Use the Central Limit theorem to find the accsptane ce set A.$A=\left\{\dots ,\dots ,\dots \right\}$b) Now tho significance level is $\alpha$ = 0.016 and the rejection set R has the form $\left\{K>{c}^{1}\right\}$Again, use tho Central Limit Theorem to find tho accaptance set A.$A=\left\{\dots ,\dots ,\dots \right\}$ Ellie Castro 2022-04-29 Answered

### I need answer full parts to the question. Show all work and be neat. Show all conditions, and p-value, conclusion, anything under the 4 step statistical process. Thanks!It can be difficult to motivate preschoolers to practice writing letters. Perhaps a reward system will do the trick, but what type of rewards work? Here are the data from a randomized experiment that compared three treatments among children in preschool. A “success" means that the child completed a worksheet in which they traced the entire alphabet in one sitting.$\begin{array}{|cccc|}\hline \text{Group}& \text{Reward}& \text{Subjects}& \text{Successes}\\ 1& \text{Choice of a small toy}& 20& 13\\ 2& \text{Choice of candy}& 24& 18\\ 3& \text{Promise of immediate recess}& 16& 10\\ \hline\end{array}$(a) Which chi-square test is appropriate in this setting? Explain your reasoning(b) State the appropriate hypotheses for performing a chi-square test in this setting.(c) The chi-square test statistic is ${\chi }^{2}=0.847$. Calculate the P-value.(d) Interpret the P-value(e) What conclusion would you draw? Eileen Garza 2022-04-29 Answered

### I assume that this problem is trivial but I am not sure what to do: In a survey of 900 people in the US a journalist says that $60\mathrm{%}$ of people support a new law. If the margin of error is $2.7\mathrm{%}$ for the percentage, what is the level of confidence? juniorychichoa70 2022-04-29 Answered

### ${s}_{p}^{2}$ is an unbiased estimator for ${\sigma }^{2}$We have, $\frac{\left({n}_{1}-1\right){s}_{1}^{2}}{{\sigma }^{2}}\sim {X}_{\left({n}_{1}-1\right)}^{2}$$\frac{\left({n}_{2}-1\right){s}_{2}^{2}}{{\sigma }^{2}}\sim {x}_{\left({n}_{2}-1\right)}^{2}$$⇒\frac{\left({n}_{1}-1\right){s}_{1}^{2}}{{\sigma }^{2}}+\frac{\left({n}_{2}-1\right){s}_{2}^{2}}{{\sigma }^{2}}\sim {x}_{\left({n}_{1}+{n}_{2}-2\right)}^{2}$$⇒Var\left({s}_{p}^{2}\right)=\frac{2{\sigma }^{4}}{{n}_{1}+{n}_{2}-2}$ komanijuuxw 2022-04-28 Answered

### Let's say I have two samples of results of two bernoulli experiments.${H}_{0}:{p}_{1}={p}_{2}$${H}_{1}:{p}_{1}\ne {p}_{2}$And I want to try to reject ${H}_{0}$ at a confidence level.I already know a proper way to solve this, but I was wondering, if I have a confidence interval for ${p}_{1}$ and ${p}_{2}$, at the same level of significance. Can I just check if the intervals overlaps each other to test this? dolovatgyp 2022-04-28 Answered

### Let $\stackrel{―}{X}$ be the mean of a random sample of size n from $N\left(\mu ,9\right)$. Find n so that $P\left(\stackrel{―}{X}-1<\mu <\stackrel{―}{X}+1\right)=.9$This problem is given at the end of a chapter in my statistics textbook concerning confidence intervals for means. Kaylee Torres 2022-04-28 Answered

### I have some problems, helpIn chi-square tests, the conventional and conservative rule is to require that the difference between the observed and expected frequency for each cell be at least 5.1. True2. False zergingk8l 2022-04-26 Answered

### Given the set: {2, 1, -3, x, 1, 2, -4}, for what x would the mean of the set be 3? Caitlyn Cole 2022-04-26 Answered

### Given the set: {2, -1, -3, x, -3, 2}, for what x would the mean of the set be 3? Elise Winters 2022-04-26 Answered

### Given the set: {12, 11, 4, 16, x, -19}, for what x would the mean of the set be 0? windpipe33u 2022-04-26 Answered

### Given the set: {1,1,1, -5, x}, for what x would the mean of the set be 1? Mekhi Cox 2022-04-26 Answered

### Given the set: {1, -11, -4, 5, x, -16}, for what x would the mean of the set be -2? Andrea Potter 2022-04-26 Answered

### Given the set: {-3, 2, -5, 1, x, 7}, for what x would the mean of the set be 3? Magdalena Norton 2022-04-26 Answered

### Given the set: {-3, -7, 18, x, -12, -9, 2}, for what x would the mean of the set be 0? Jaidyn Cook 2022-04-26 Answered

### Given the set: {-2, 5, -6, 8, x}, for what x would the mean of the set be 1? Araceli Soto 2022-04-26 Answered

### Given a set {11, x, -44, 1}, for what x would the mean be 4?

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