#### Didn’t find what you are looking for? Normal distributions ### Consider two independent populations that are normally distributions. A simple random sample of $$\displaystyle{n}_{{1}}={41}$$ from the first population showed $$\displaystyle\overline{{x}}_{{11}}={33}$$, and a simple random of size $$\displaystyle{n}_{{2}}={48}$$ from the second population showed $$\displaystyle\overline{{x}}_{{2}}={32}$$ Suppose $$\displaystyle{s}_{{1}}={9}{s}_{{1}}={9}{\quad\text{and}\quad}{s}_{{2}}={10}{s}_{{2}}={10}$$, find a 98% confidence interval for $$\displaystyle\mu_{{1}}−\mu_{{2}}\mu_{{1}}-\mu_{{2}}$$. (Round answers to two decimal places.) margin of error-? lower limit-? upper limit-?

Data distributions ### What is the difference between a normal profile of a random variable and normal pdf of a random variable.

Study design ### To find:Whether the experiment is an observational or a designed experiment.

Study design ### A proposed study design is to leave 100 questionnaires by the checkout line in a student cafeteria. The questionnaire can be picked up by any student and returned to the cashier. Explain why this volunteer sample is a poor study design.

Two-way tables ### Using data from the 2000 census, a random sample of 348 U.S. residents aged 18 and older was selected. The two-way table summarizes the relationship between marital status and housing status for these residents. $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{l}{\left|{c}\right|}{c}{\mid}{c}\right\rbrace}&{M}{a}{r}{r}{i}{e}{d}&{N}{o}{t}{m}{a}{r}{r}{i}{e}{d}&{T}{o}{t}{a}{l}\backslash{h}{l}\in{e}{O}{w}{n}&{172}&{82}&{254}\backslash{h}{l}\in{e}{R}{e}{n}{t}&{40}&{54}&{94}\backslash{h}{l}\in{e}{T}{o}{t}{a}{l}&{212}&{136}&{348}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$

Scatterplots ### A nutritionist collects the weight of college students in the first semester, then again in the second semester. What is the best way to visually present this data? a) Line Graphs b) Scatterplots c) Bar Graphs d) Pie Charts

Normal distributions ### Explain some of the important characteristics of a normal distribution.

Data distributions ### We have a set of n-elements (A), and a set of m-elements (B). $$\displaystyle{n}\ge{0}$$ $$\displaystyle{m}\ge{0}$$ Find how many relations there're from A to B.

Scatterplots ### Make a scatterplot for the data. Height and Weight of Females Height (in.): 58, 60, 62, 64, 65, 66, 68, 70, 72 Weight (lb): 115, 120, 125, 133, 136, 115, 146, 153, 159

Normal distributions ### A normal distribution has $$\mu = 30$$ and $$\sigma = 5$$. (c)Find the raw score corresponding to $$z =-2$$.

Scatterplots ### Match the values of r with the accompanying scatterplots 0.723,-0.353,0.353,0.998 and -0.998 scatterplots 1,2,3,4,5 Two-way tables ### 1950 randomly selected adults were asked if they think they are financially better off than their parents. The following table gives the two-way classification of the responses based on the education levels of the persons included in the survey and whether they are financially better off, the same as, or worse off than their parents $$\begin{array}{|c|c|c|}\hline &\text{Less Than High School}&\text{High School}&\text{More Than High School}\\\hline \text{Better off} &140&440&430\\ \hline \text{Same as}&60&230&110\\ \hline \text{Worse off}&180&280&80\\ \hline\end{array}\\$$ Suppose one adult is selected at random from these 1950 adults. Find the following probablity. Round your answer to three decimal places. $$P(\text{more than high school or worse off})=?$$

Scatterplots ### Sketch a scatterplot where the association is linear, but the correlation is close to [r = 0].

Normal distributions ### Consider the marks of all 1st-year students on a statistics test. If the marks have a normal distribution with a mean of 72 and a standard deviation of 9, then the probability that a random sample of 10 students from this group have a sample mean between 71 and 73 is?

Two-way tables ### How are the smoking habits of students related to their parents' smoking? Here is a two-way table from a survey of student s in eight Arizona high schools: $$\begin{array}{c|c}&\text{Student smokes}&\text{Student does not smoke}&\text{Total}\\\hline\text{Both parents smoke}&400&1380&400+1380=1780\\\hline\text{One parent smokes}&416&1823&416+1823=2239\\\hline\text{Neither parent smokes}&188&1168&188+1168=1356\\\hline\text{Total}&400+416+188=1004&1380+1823+1168=4371&1004+4371=5375\end{array}$$ (a) Write the null and alternative hypotheses for the question of interest. (b) Find the expected cell counts. Write a sentence that explains in simple language what "expected counts" are. (c) Find the chi-square statistic, its degrees of freedom, and the P-value. (d) What is your conclusion about significance?

Two-way tables ### When performing a $$\displaystyleχ^{{2}}$$ test of independent in a contingency table with r rows and c columns, determine the upper-tail critical value of the test statistic in each of the following circumstances: a. α=0.05, r=4 rows, c=5 columns b. α=0.01, r=4 rows, c=5 columns c. α=0.01, r=4 rows, c=6 columns d. α=0.01, r=3 rows, c=6 columns e. α=0.01, r=6 rows, c=3 columns

Normal distributions ### $$\displaystyle{\left(\mu{1}-\mu{2}\right)}$$ For two normal distributions Obtain the appropriate point estimator

Study design ### In the 1970s a study was conducted in Philadelphia in which 500 cases were randomly assigned to treatments for the common cold: 250 subjects received the medication and 250 received a placebo. A total of 383 patients improved within 24 hours. Of those who received the medication 241 improved within 24 hours and of those who received the placebo 142 improved within 24 hours. A test of significance was conducted on the following hypotheses. $$\displaystyle{H}_{{o}}$$: The rates for the two treatments are equal. $$\displaystyle{H}_{{a}}$$: The treatment of medication has a higher improvement rate. This test resulted in a p-value of 0.0761. a.) Interpret what this p-value measures in the context of this study. b.) Based on this p-value and study design, what conclusion should be drawn in the context of this study? Use a significance level of $$\displaystyle\alpha={0.05}$$. c.) Based on your conclusion in part (b), which type of error, Type I or Type II, could have been made? What is one potential consequence of this error?

Study design  