# Get help with college statistics

Recent questions in College Statistics
Alternate coordinate systems

### Systems of Inequalities Graph the solution set of the system if inequalities. Find the coordinates of all vertices, and determine whether the solution set is bounded. $$\displaystyle{b}{e}{g}\in{\left\lbrace{c}{a}{s}{e}{s}\right\rbrace}{y}{<}{9}-{x}^{{{2}}}\backslash{y}\geq{x}+{3}{e}{n}{d}{\left\lbrace{c}{a}{s}{e}{s}\right\rbrace}$$

Alternate coordinate systems

### 4.(a) Sketch the region of solutions of the following systems of inequalities: $$\displaystyle{2}?+{3}?≤{12}$$ $$\displaystyle−?+{2}?{<}{4}$$ $$\displaystyle?≥{0}$$ $$\displaystyle?≥{0}$$ b. List the coordinates of all of the corner points: c Which corner point would maximize the equation $$\displaystyle?={5}?+{3}??$$

Confidence intervals

### The standard deviation for a population is $$\displaystyle\sigma={14.8}$$. A sample of 21 observations selected from this population gave a mean equal to 139.05. The population is known to have a normal distribution. Round your answers to two decimal places. a) Make a $$\displaystyle{99}\%$$ confidence interval for $$\displaystyle\mu$$. ( Enter your answer; $$\displaystyle{99}\%$$ confidence interval, lower bound ,Enter your answer; $$\displaystyle{99}\%$$ confidence interval, upper bound ) b) Construct a $$\displaystyle{97}\%$$ confidence interval for $$\displaystyle\mu$$. ( Enter your answer; $$\displaystyle{97}\%$$ confidence interval, lower bound ,Enter your answer; $$\displaystyle{97}\%$$ confidence interval, upper bound ) c) Determine a $$\displaystyle{95}\%$$ confidence interval for $$\displaystyle\mu$$. ( Enter your answer; $$\displaystyle{95}\%$$ confidence interval, lower bound ,Enter your answer; $$\displaystyle{95}\%$$ confidence interval, upper bound )

Confidence intervals

### A statistics practitlioner took a randoml sample of 54 observations form a population whose standard deviation is 29 and computed the sample mean to be 97. Note: For each confidence interval, enter your answer in the forem (LCL, UCL). You must include the parentheses and the comma between the confidence limits. A) Estimate the population mean with $$\displaystyle{95}\%$$ confidence. B) Estimate the population mean with $$\displaystyle{90}\%$$ confidence. C) Estimate the population mean with $$\displaystyle{99}\%$$ confidence.

Confidence intervals

### It was observed that 30 of the 100 randomly selected students smoked. Find the confidence interval estimate of $$\displaystyle{95}\%$$ confidence level for $$\displaystyle\pi$$ ratio of smokers in the population. a) $$\displaystyle{P}{\left({0.45}{<}{p}{<}{0.78}\right)}={0.95}$$ b) $$\displaystyle{P}{\left({0.11}{<}{p}{<}{0.28}\right)}={0.95}$$ c) $$\displaystyle{P}{\left({0.51}{<}{p}{<}{0.78}\right)}={0.95}$$ d) $$\displaystyle{P}{\left({0.21}{<}{p}{<}{0.59}\right)}={0.95}$$ e) $$\displaystyle{P}{\left({0.21}{<}{p}{<}{0.39}\right)}={0.95}$$

Confidence intervals

### Based on a simple random sample of 1300 college students, it is found that 299 students own a car. We wish to construct a $$\displaystyle{90}\%$$ confidence interval to estimate the proportions ? of all college students who own a car. A) Read carefully the text and provide each of the following: The sample size $$\displaystyle?=$$ from the sample, the number of college students who own a car is $$\displaystyle?=$$ the confidence level is $$\displaystyle{C}{L}=$$ $$\displaystyle\%$$. B) Find the sample proportion $$\displaystyle\hat{{?}}=$$ and $$\displaystyle\hat{{?}}={1}−\hat{{?}}=$$

Confidence intervals

### Two different analytical tests can be used to determine the impurity level in steel alloys. Nine specimens are tested using both procedures, and the results are shown in the following tabulation. $$\begin{array}{|c|c|}\hline Specimen & Test-1 & Test-2 \\ \hline 1 & 1.2 & 1.4 \\ \hline 2 & 1.6 & 1.7 \\ \hline 3 & 1.5 & 1.5 \\ \hline 4 & 1.4 & 1.3 \\ \hline 5 & 1.8 & 2.0 \\ \hline 6 & 1.8 & 2.1 \\ \hline 7 & 1.4 & 1.7 \\ \hline 8 & 1.5 & 1.6 \\ \hline 9 & 1.4 & 1.5 \\ \hline \end{array}$$ Find the $$\displaystyle{95}\%$$ confidence interval for the mean difference of the tests, and explain it.

Confidence intervals

### You are interested in finding a $$\displaystyle{95}\%$$ confidence interval for the mean number of visits for physical therapy patients. The data below show the number of visits for 14 randomly selected physical therapy patients. Round answers to 3 decimal places where possible. $$\begin{array}{|c|c|}\hline 9 & 6 & 10 & 15 & 19 & 6 & 23 & 26 & 19 & 16 & 11 & 25 & 16 & 11 \\ \hline \end{array}$$ a) To compute the confidence interval use a t or z distribution. b) With $$\displaystyle{95}\%$$ confidence the population mean number of visits per physical therapy patient is between "?" and "?" visits. c) If many groups of 14 randomly selected physical therapy patients are studied, then a different confidence interval would be produced from each group. About "?" percent of these confidence intervals will contain the true population mean number of visits per patient and about "?" percent will not contain the true population mean number of visits per patient.

Confidence intervals

### (a) Seek power series solutions of the given differential equation about the given point $$x_0$$, find the recurrence relation. (b) Find the first tour terms in each of two solutions $$\displaystyle{y}_{{{1}}}{\quad\text{and}\quad}{y}_{{{2}}}$$ (unless the series terminates sooner). (c) By evaluating the Wronskian $$\displaystyle{W}{\left({y}_{{{1}}}{y}_{{{2}}}\right)}{\left({x}_{{{0}}}\right)}$$, show that $$\displaystyle{y}_{{{1}}}{\quad\text{and}\quad}{y}_{{{2}}}$$ form a fundamental set of solutions. (d) It possible, find the general term in each solution $$\displaystyle{\left({1}+{x}^{{{2}}}\right)}{y}\text{}{4}{x}{y}'+{6}{y}={0},{x}_{{{0}}}={0}$$

Comparing two groups

### how many ways can 9 peoples be assigned to 2-triple, 1-double and 1-single room?

Confidence intervals

### A sample selected from a population gave a sample proportion equal to 0.59 . Round your answers to three decimal places. a) Make a $$\displaystyle{95}\%$$ confidence interval for p assuming $$\displaystyle{n}={150}$$ ( Enter your answer; confidence interval assuming $$\displaystyle{n}={150}$$, lower bound ,Enter your answer; confidence interval assuming $$\displaystyle{n}={150}$$, upper bound ) b) Construct a $$\displaystyle{95}\%$$ confidence interval for p assuming $$\displaystyle{n}={600}$$. ( Enter your answer; confidence interval assuming $$\displaystyle{n}={600}$$, lower bound ,Enter your answer; confidence interval assuming $$\displaystyle{n}={600}$$, upper bound ) c) Make a $$\displaystyle{95}\%$$ confidence interval for p assuming $$\displaystyle{n}={1275}$$. ( Enter your answer; confidence interval assuming $$\displaystyle{n}={1275}$$, lower bound ,Enter your answer; confidence interval assuming $$\displaystyle{n}={1275}$$, upper bound )

Confidence intervals

### Express the confidence interval $$\displaystyle{172.3}{<}\mu{<}{229.1}$$ in the form of $$\displaystyle\overline{{{x}}}\pm{M}{E}.$$

Confidence intervals

### Refer to the accompanying data display that results from a sample of airport data speeds in Mbps. Complete parts (a) through (c) below. a. Express the confidence interval in the format that uses the "less than" symbol. Given that the original listed data use one decimal place, round the confidence intervals limits accordingly. $$\displaystyle{13.05}{M}{b}{p}{s}{<}\mu{<}{22.15}$$ Mbps b. Identify the best point estimate of $$\displaystyle\mu$$ and the margin of error. The point estimate of $$\displaystyle\mu$$ is 17.60 Mbps. The margin of error is $$\displaystyle{E}=?$$ Mbps.

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 - ?$$\displaystyle{<}{p}{<}$$?

Confidence intervals

### The article “Analysis of the Modeling Methodologies for Predicting the Strength of Air-Jet Spun Yarns” (Textile Res. J., 1997: 39–44) reported on a study carried out to relate yarn tenacity $$\displaystyle{\left({y},\ \in\ {\frac{{{g}}}{{{t}{e}{x}}}}\right)}$$ to yarn count $$\displaystyle{\left({x}_{{{1}}},\ \in\ {t}{e}{x}\right)}$$, percentage polyester $$\displaystyle{\left({x}_{{{2}}}\right)}$$, first nozzle pessure $$\displaystyle{\left({x}_{{{3}}},\ \in\ {\frac{{{k}{g}}}{{{c}{m}^{{{2}}}}}}\right)}$$, and second nozzle pressure $$\displaystyle{\left({x}_{{{4}}},\ \in\ {\frac{{{k}{g}}}{{{c}{m}^{{{2}}}}}}\right)}$$ The estimate of the constant term in the corresponding multiple regression equation was 6.121. The estimated coefficients for the four predictors were -0.082, 0.113, 0.256, and -0.219, respectively, and the coefficient of multiple determination was 0.946 a) Assuming that the sample size was $$\displaystyle{n}={25}$$, state and test the appropriate hypotheses to decide whether the fitted model specifies a useful linear relationship between the dependent variable and at least one of the four model predictors. b) Again using $$\displaystyle{n}={25}$$, calculate the value of adjusted $$\displaystyle{R}^{{{2}}}$$. c) Calculate a 99% confidence interval for true mean yarn tenacity when yarn count is 16.5, yarn contains 50% polyester, first nozzle pressure is 3, and second nozzle pressure is 5 if the estimated standard deviation of predicted tenacity under these circumstances is 0.350.

Confidence intervals

### Using 64 randomly selected phone calls, the average call length was calculated to be 4.2 minutes. It is known from previous studies that the variance of the length of phone calls is $$\displaystyle{1.44}\min^{{{2}}}$$. Assuming that the length of calls has a normal distribution a) estimate an interval estimate of the length of a telephone conversation at the 0.95 confidence level b) confidence 0.99 c) Compare the length of the two intervals and explain how the length of the interval depends on the confidence level.

Confidence intervals

### A study a local high school tried to determine the mean height of females in the US. A study surveyed a random sample of 125 females and found a mean height of 64.5 inches with a standard deviation of 5 inches. Determine a $$\displaystyle{95}\%$$ confidence interval for the mean. $$\begin{array}{|c|c|} \hline \text{Confidence Interval} & z \\ \hline 80\% & 1.282 \\ \hline 85\% & 1.440\\ \hline 90\% & 1.645\\ \hline 95\% & 1.960\\ \hline 99\% & 2.576\\ \hline 99.5\% & 2.807\\ \hline 99.9\% & 3.291\\ \hline \end{array}$$

Confidence intervals

### The monthly incomes for 12 randomly selected​ people, each with a​ bachelor's degree in​ economics, are shown on the right. Complete parts​ (a) through​ (c) below. Assume the population is normally distributed. a) Find the sample mean. b) Find the sample standard deviation c) Construct a $$\displaystyle{95}\%$$ confidence interval for the population mean $$\displaystyle\mu$$. A $$\displaystyle{95}\%$$ confidence interval for the population mean is $$\begin{array}{|c|c|}\hline 4450.42 & 4596.96 & 4366.46 \\ \hline 4455.62 & 4151.52 & 3727.77 \\ \hline 4283.26 & 4527.94 & 4407.68 \\ \hline 3946.49 & 4023.61 & 4221.73\\ \hline \end{array}$$

Alternate coordinate systems