2.)Provide a complete solution with all work shown.A rural county hospital offers several health services. The hospital administrators conducted a poll to determine whether the residents’ satisfaction with the available services depends on their gender. A random sample of 1,000 adult county residents was selected. The gender of each respondent was recorded and each was asked whether he or she was satisfied with the services offered by the hospital. The resulting data are shown in the table below.MaleFemaleTotalSatisfied384416800Not Satisfied80120200Total4645361,000a. Using a significance level of 0.05, conduct an appropriate test to determine if, for adult residents of this county, there is an association between gender and whether or not they were satisfied with services offered by the hospital.b. Isa reasonable estimate for the proportion of all adult county residents who are satisfied with the services offered by their hospital? Explain why or why not.3.)An experiment was performed to examine the personal goals of children in grades 4, 5, and 6. A random sample of students was selected for each of the three grades from schools in Alabama. The students received a questionnaire regarding achieving personal goals. They were asked what they would most like to do at school: make good grades, be good at sports, or be popular.GenderMake good gradesBe popularBe good in sportsBoys963294Girls2954540Using the above data, what is the proportion of boys who chose the goal “Make good grades”?A.) .22B.) .43C.) .96D.) .16E.) .254.)An experiment was performed to examine the personal goals of children in grades 4, 5, and 6. A random sample of students was selected for each of the three grades from schools in Alabama. The students received a questionnaire regarding achieving personal goals. They were asked what they would most like to do at school: make good grades, be good at sports, or be popular.GenderMake good gradesBe popularBe good in sportsBoys963294Girls2954540Suppose we wish to test the null hypothesis that there are no differences among the proportion of boys and the proportion of girls choosing each of the three personal goals. Under the null hypothesis, what is the expected number of boys that would select “Make good grades”?A.) 96B.) 196C.) 222D.) 305E.) 1445.)Do men and women treat male and female children differently? An observational study was conducted near the primate exhibit at the San Diego Zoo on weekends in 1988. The data are from 39 groups of three, one adult female, one adult male, and one toddler, in which the toddler was being carried.Sex of toddlerSex of toddlerSex of adultcarrying toddlerMaleFemaleMale817Female68Using the above data, what is the proportion of times a male adult was carrying the toddler?A.) .32B.) .36C.) .57D.) .17E.) .646.)Do men and women treat male and female children differently? An observational study was conducted near the primate exhibit at the San Diego Zoo on weekends in 1988. The data are from 39 groups of three, one adult female, one adult male, and one toddler, in which the toddler was being carried.Sex of toddlerSex of toddlerSex of adultcarrying toddlerMaleFemaleMale817Female68What is the proportion of all male toddlers that were carried by the male adult?A.) .32B.) .36C.) .64D.) .17E.) .577.)Although Puerto Rico is a territory of the United States, there are many cultural differences between the states and the island. These differences include the way that the consumers handle problems with purchases. Two researchers surveyed owners of VCRs in the Northeast U.S. and in Puerto Rico. They asked those who had experienced problems with their VCRs whether they had complained.ComplainedNortheast U.S.Puerto RicoNo9433Yes33064Which of the following is the appropriate degrees of freedom for the chi-square statistic?A.) 1B.) 2C.) 3D.) 4E.) 108.)Although Puerto Rico is a territory of the United States, there are many cultural differences between the states and the island. These differences include the way that the consumers handle problems with purchases. Two researchers surveyed owners of VCRs in the Northeast U.S. and in Puerto Rico. They asked those who had experienced problems with their VCRs whether they had complained.ComplainedNortheast U.S.Puerto RicoNo9433Yes33064Which cell contributes most to the chi-square statistic?A.) Americans in the states that did not complainB.) Americans in the states that complainedC.) Puerto Ricans that complained D.) Puerto Ricans that did not complainE.) None of the above9.)Could mud wrestling be the cause of a rash contracted by Washington State University students in the spring of 1992? Physicians at the WSU student health center wondered this when one male and six female students complained of rashes after participating in a mud wrestling event. Questionnaires were sent to all students in the residence halls that participated in the event. The questionnaire asked about the appearance of a rash and about attendance at the event. The results are summarized below:MenWomenDeveloped Rash1212No Rash3812Using the above data, which of the following is the best conclusion?A.) Mud wrestling causes a rash, especially for womenB.) There is absolutely no evidence of any relation between the gender of an individual attending the event and the subsequent development of a rash.C.) Development of the rash is a real possibility if you attend mud wrestling events, especially if you attend them on a regular basis.D.) There appears to be evidence of an association between the gender of an individual attending the event and development of a rash.E.) You will develop the rash only if you attend every mud wrestling event and actually wrestle.10.)Provide a complete solution with all work shown.John believes that as he increases his walking speed, his pulse rate will increase. He wants to model this relationship. John records his pulse rate, in beats per minute (bpm), while walking at each of seven different speeds, in miles per hour (mph). A scatterplot and regression output are shown below.PredictorCoefSE CoefTPConstant63.4572.38726.580.000Speed16.28090.819219.880.000S = 3.087R-Sq = 98.7%R-Sq (adj) = 98.5%Analysis of VarianceSourceDFSSMSFPRegression13763.23763.2396.130.000Residual547.69.5Total63810.9a. Using the regression output, write the equation of the fitted regression line.b. Do your estimates of the slope and intercept parameters have meaningful interpretations in the context of this question? If so, provide interpretations in this context. If not, explain why not.c. John wants to provide a 98% confidence interval for the slope parameter in his final report. Compute the margin of error that John should use. Assume that conditions for inference are satisfied.11.)Do the levels of fear in children change over time? If so, in what ways? Very little research has been done on the prevalence and persistence of fears in children. Researchers surveyed a group of third and fourth grade children and asked them to rate their level of fear about a variety of situations. After two years the children again completed the same survey. The researchers calculated the mean fear rating for each child in both years and were interested in the relation between these ratings. The least-squares regression line for the data, with 89 mean fear ratings as the explanatory variable and 91 mean fear ratings as the response variable, is given below.Dependent variable is 91 meansR squared = 27.4%S = 0.2374 with 94 ? 2 = 92 degrees of freedomVariableCoefficients.e. of coefficientt-ratioP-valueConstant0.8779170.11847.42Â¡Ã 0.000189 means0.3979110.06765.89Â¡Ã 0.0001Using the above data, approximately what is the intercept of the least squares regression line?A.) .40B.) .44C.) .88D.) .12E.) .0712.)Do the levels of fear in children change over time? If so, in what ways? Very little research has been done on the prevalence and persistence of fears in children. Researchers surveyed a group of third and fourth grade children and asked them to rate their level of fear about a variety of situations. After two years the children again completed the same survey. The researchers calculated the mean fear rating for each child in both years and were interested in the relation between these ratings. The least-squares regression line for the data, with 89 mean fear ratings as the explanatory variable and 91 mean fear ratings as the response variable, is given below.Dependent variable is 91 meansR squared = 27.4%S = 0.2374 with 94 ? 2 = 92 degrees of freedomVariableCoefficients.e. of coefficientt-ratioP-valueConstant0.8779170.11847.42Â¡Ã 0.000189 means0.3979110.06765.89Â¡Ã 0.0001Approximately what is a 95% confidence interval for the slope of the least squares regression line?A.) 0.26, 0.54B.) 0.76, 1C.) 0.74, 1.02D.) 0.33, 0.47E.) 0.38, 0.4213.)At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are bundled in clothes to restrict their movement? Data was collected from parents who brought their babies to New York University Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported ages (in weeks) at which their child was first able to crawl a distance of four feet within one minute. The researchers also recorded the average outdoor temperature (in F) 6 months after the babies’ date of birth. The resulting data were grouped by month of birth and all data for babies born on a given month averaged together. If we fit the least-squares line to the 12 data points (one for each month), we obtain the following results from a software package. Notice that the temperature given is taken as the explanatory variable and crawling age as the response variable.Dependent variable is the average crawling ageR squared = 49.0%S = 1.319 with 12 ? 2 = 10 degrees of freedomVariableCoefficientS.E. of coefficientConstant35.67811.318Temperature-0.0777390.0251What is the approximate slope of the least-squares regression line?A.) 35.68B.) 1.32C.) .01D.) -.08E.) -.5814.)At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are bundled in clothes to restrict their movement? Data was collected from parents who brought their babies to New York University Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported ages (in weeks) at which their child was first able to crawl a distance of four feet within one minute. The researchers also recorded the average outdoor temperature (in F) 6 months after the babies? date of birth. The resulting data were grouped by month of birth and all data for babies born on a given month averaged together. If we fit the least-squares line to the 12 data points (one for each month) we obtain the following results from a software package. Notice that the temperature given is taken as the explanatory variable and crawling age as the response variable.Dependent variable is the average crawling ageR squared = 49.0%S = 1.319 with 12 ? 2 = 10 degrees of freedomVariableCoefficientS.E. of coefficientConstant35.67811.318Temperature-0.0777390.0251Suppose we wish to test the following hypotheses:H0: the slope of the least squares regression line = 0HA: the slope of the least squares regression line0What is the value of the t-statistic for this test?A.) 35.68B.) 27.1C.) -3.10D.) -.08E.) 2.76

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