 # College Statistics & Probability Questions and Answers

Recent questions in College Statistics Deven Livingston 2022-04-26 Answered

### Given a set {13, x, -1, 11}, for what x would the mean of the set be 3? airesex2 2022-04-26 Answered

### Given a set {-3, x,3,4,6,5, -3, 2}, for what x would the mean of the set be -1? occhei042 2022-04-26 Answered

### Given a set {-3, x, 3,4,6}, for what x would the mean of the set be -11? dreangannaa 2022-04-26 Answered

### Given a set {-2, x, -3, -4, 1, 15, 22, 2}, for what x would the mean of the set be -12? g2esebyy7 2022-04-25 Answered

### Simple Linear Regression - Difference between predicting and estimating?Here is what my notes say about estimation and prediction:Estimating the conditional mean"We need to estimate the conditional mean ${\beta }_{0}+{\beta }_{1}{x}_{0}$ at a value ${x}_{0}$, so we use $\stackrel{^}{{Y}_{0}}=\stackrel{^}{{\beta }_{0}}+\stackrel{^}{{\beta }_{1}}{x}_{0}$ as a natural estimator." here we getwith a confidence interval for $E\left({Y}_{0}\right)={\beta }_{0}+{\beta }_{1}{x}_{0}$ is$\left(\stackrel{^}{{b}_{0}}+\stackrel{^}{{b}_{1}}{x}_{0}-cs\sqrt{{h}_{00}},\stackrel{^}{{b}_{0}}+\stackrel{^}{{b}_{1}}{x}_{0}+cs\sqrt{{h}_{00}}\right)$where $c={t}_{n-2,1-\frac{\alpha }{2}}$ Where these results are found by looking at the shape of the distribution and at $E\left(\stackrel{^}{{Y}_{0}}\right)$ and $var\left(\stackrel{^}{{Y}_{0}}\right)$Predicting observations"We want to predict the observation ${Y}_{0}={\beta }_{0}+{\beta }_{1}{x}_{0}+{ϵ}_{0}$ at a value ${x}_{0}$"Hence a prediction interval is of the form$\left(\stackrel{^}{{b}_{0}}+\stackrel{^}{{b}_{1}}{x}_{0}-cs\sqrt{{h}_{00}+1},\stackrel{^}{{b}_{0}}+\stackrel{^}{{b}_{1}}{x}_{0}+cs\sqrt{{h}_{00}+1}\right)$ Kymani Shepherd 2022-04-25 Answered

### Probability vs ConfidenceMy notes on confidence give this question:An investigator is interested in the amount of time internet users spend watching TV a week. He assumes $\sigma =3.5$ hours and samples $n=50$ users and takes the sample mean to estimate the population mean $\mu$.Since $n=50$ is large we know that $\frac{\stackrel{―}{X}-\mu }{\frac{\sigma }{\sqrt{n}}}$ approximates the Standard Normal. So, with probability $\alpha =0.99$, the maximum error of estimate is $E={z}_{\frac{\alpha }{2}}×\frac{\sigma }{\sqrt{n}}\approx 1.27$ hours.The investigator collects that data and obtain $\stackrel{―}{X}=11.5$ hours. Can he still assert with 99% probability that the error is at most 1.27 hours?With the answer that:No he cannot, because the probability describes the method/estimator, not the result. We say that "we conclude with 99% confidence that the error does not exceed 1.27 hours."I am confused. What is this difference between probability and confidence? Is it related to confidence intervals? Is there an intuitive explanation for the difference? etudiante9c2 2022-04-25 Answered

### Given the set: {5,3,6,-2,5,6, -1,x}, for what x would the mean of the set be 0? Troszokd95 2022-04-25 Answered

### Given the set: {5, x, 11, -3, -12, 19, 10}, for what x would the mean of the set be 0? Dereon Guzman 2022-04-25 Answered

### Given the set: {-1, 6,4,11,x, -7}, for what x would the mean of the set be 1? Dania Robbins 2022-04-25 Answered

### Given the set: {-2, 10, -8, -14, x, 7, -6}, for what x would the mean of the set be -8? Hugh Walls 2022-04-25 Answered

### Given a set {4, -2, -12, 5, x}, for what x would the mean of the set be -5? Ricardo Berger 2022-04-25 Answered

### Given a set {9,3,4,6,x,6,1,-4}, for what x would the mean of the set be -32? albusgks 2022-04-24 Answered

### IQ scores among the general population have a mean of 100 and a standard deviation of 15. A researcher claims that the standard deviation, o, of IQ scores for males is less than 15. A random sample of 19 IQ scores for males had a mean of 101 and a standard deviation of 10. Assuming that IQ scores for males are approximately normally distributed, is there significant evidence (at the 0.05 level of significance) to conclude that the researcher's claim is correct?Perform a one-tailed test. Then complete the parts below.Carry your intermediate computations to three or more decimal places and round your answers as specified below. (If necessary, consult a list of formulas.)(a) State the null hypothesis ${H}_{0}$, and the alternative hypothesis ${H}_{1}$,${H}_{0}$:${H}_{1}$:(b) Determine the type of test statistic to use.(c) Find the value of the test statistic. (Round to three or more decimal places.)(d) Find the critical value. (Round to three or more decimal places.)(e) Can we support the claim that the standard deviation of IQ scores for males is less than 15?a. Yesb. No Dashawn Clark 2022-04-24 Answered

### In your own words, distinguish between measures of association and tests of statistical significance. Abraham Bradley 2022-04-24 Answered

### In which of the following situations should the chi-square Test for Homogeneity be used?Select the correct answer below:A professor wants to determine if the students in each of her two sections had the same distribution of grades. She records the grade distribution for each section and compares the two distributions.A survey company puts out a survey asking people two questions. First, it asks if a person owns a car or not. Second, it asks whether or not the person supports an upcoming environmental protection bill. The data are recorded in a contingency table. The company wants to determine if support for the bill is independent of car ownership.A professor expects that the grades on a recent exam are normally distributed with a mean of 80 and a standard deviation of 10. She records the actual distribution of grades and wants to compare it to the normal distribution. tefoldaavv 2022-04-24 Answered

### In the following table, likely voters’ preferences of two candidates are cross-classified by gender.For the chi-square test of independence, the value of the test statistic is:a. 2.34b. 1.62c. 3.25d. 4 surgerh7a 2022-04-24 Answered

### In each of Exercises, we have provided a sample mean, sample size, and population standard deviation. In each case, use the one-mean z-test to perform the required hypothesis test at the 5% significance level.x = 24, n = 15, $\sigma$ = 4, H0: $\mu$ = 22, Ha: $\mu$ > 22 Davon Trujillo 2022-04-24 Answered

### In conducting a significance test, is it easier or harder to reject the null hypothesis when the sample size is 1,500 compared to a sample size of 1,000?a) easierb) harder micelije1mw 2022-04-24 Answered

### In a chi-square test for goodness of fit, which of the following is used to compute the degrees of freedom?a. The number of cells in the tableb. The number of categories for the variable plus 1c. The number of rows times the number of columnsd. The number of categories for the variable minus 1 acceloq3c 2022-04-24 Answered

### If you are already certain that a null hypothesis is false, then:Significance testing provides no useful information since all it does is reject a null hypothesis.Significance testing is informative because you still need to know whether an effect is significant even if you know the null hypothesis is false.When a difference is significant you can draw a confident conclusion about the direction of the effect.

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