If we are testing for the difference between the means of 2 independent populations with samples of n1=20 and n2=20, the number of degrees of freedom is equal to O 18 O 19 O 38 O 39
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- A researcher is interested in the amount of sleep an individual receives after consuming a sleeping aid (Melatonin, Valerian root, and Placebo). The researcher randomly selects individuals into either group. However, some individuals drop out of the study which results in unequal sample sizes. Melatonin Valerian Placebo n=6 n=10 n=4 N=20 M=14 M=13 M=9 G=250 T=84 T=130 T=36 ΣX2=3377 SS=60 SS=90 SS=37 a. Using symbols, state the hypotheses for a two-tailed test with α=0.05. b. Locate the critical region. In doing so, determine the degrees of freedom values. c. Calculate the F-ratio.The Mathematics Department in a certain university is conducting a study to determine how long it takes it graduates to find a job. A sample of 26 graduates was surveyed and it was found that the average time it has taken a graduate to find a new job is 3.5 months with a standard deviation of 1.5 months. Is there sufficient evidence to conclude that the graduates of this department take on the average at most three months to find a job at 10% level of significance? P-value: Decision: Conclusion:A sample of 90 items from population 1 has a sample variance of 6, while a sample of 70 items from population 2 has a sample variance of 10. If we test whether the variances of the two populations are equal, the test statistic will have a value of O a. 0.78 O b. 1.67 O c.0.60 O d. 1.29
- A researcher studying air quality in a metropolitan city is interested in testing the claim that less than 20% of people smoke cigarettes to test this claim the researcher collects the following data on a sample of 700 adults and 110 of them smoke cigarettes the following is the data from the study. Sample size= 700 adults Alternative hypothesis= ha:pIn a random sample of 320 cars driven at low altitude, 40 of them exceeded the standard 10 grams of particulate pollution per gallon of fuel consumed. In another independent random sample of 80 cars driven at high altitude, 20 of them exceeded the standard. Let P 1be the true proportion of cars that exceed the standard in low altitudes and P 2be the true proportion of cars that exceed the standard in high altitudes. What is the test statistic for testing this hypothesis.The number of points held by random samples of the NHL's highest scorers of both the Eastern Conference and the Western Conference is shown. At the 0.05 level of significance, can it be concluded that there is a difference in means based on theses data: Eastern Conference Western Conference 83 60 75 58 77 59 72 58 78 59 70 58 37 57 66 55 62 61 59 61 What is the appropriate null hypothesis for this problem? (u= population mean for this problem) What is the critical Value? What is the test statistics? What is the decision?
- What is the value of the sample test statistic? (Test the difference p₁ - P2. Do not use rounded values. Round your final answer to two decimal places.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. 0-3 -2 -2 -1 -1 0 Read It 0 1 1 Watch it 2 2 3 0-3 ^ -1 0 1 -2 -2 -1 0 1 O At the a = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. 2 2 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. O At the a= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. 3…A company attempts to evaluate the potential for a new bonus plan and decides to use the bonus plan for a trial period. The weekly sales volume achieved by a sample of 4 salespersons before and after implementing the bonus plan is shown below. (For the following matched samples, let the difference d = After – Before; let population men Before = μ1, population mean After = μ2) Weekly Sales (in units) Salesperson Before After 1 48 44 2 48 40 3 38 36 4 44 50 Assume the population of differences is normally distributed. Use α = 0.05 and test to see if the bonus plan will result in an increase in the mean weekly sales for the company. What is your conclusion?Researchers studying osteoporosis (bone loss) suspected that women over the age of 50 in the United States are diagnosed with the disease more often than women over 50 in Mexico. They took a random sample of 200 women over the age of 50 from each country. Here are the results: Diagnosed with osteoporosis? US Mexico Yes 40 20 No 160 180 Total 200 200 The researchers want to use these results to test Ho: pus – PM = 0 versus H,: Pus – PM > 0. Assume that all conditions have been met. What is the P-value associated with these sample results? P-value is greater than or equal to 0.20 0.05 is less than or equal to the P- value < 0.10 0.10 is less than or equal to the P- value < 0.20 P-value < 0.01 0.01 is less than or equal to the P- value < 0.05
- 2. The difference between the two groups has been declared statistically significant at the a = 0.05 level. Use the "No Adolescent Marijuana" group to determine a suitable p0, and then test the hypothesis: HO: p ≤ p0 HA: p > p0 where p is the population proportion (conceptualized) of all adolescent marijuana users who would develop schizophrenia. Show all your work. Are the results statistically significant as claimed? Make sure you report the standard score, a p-value, your conclusion, and a comment on what statistical risk has been taken and controlled for in this testing process. Percent Developing Schizophrenia 7%- 6%- 5%- 4% 3%- 2%- 1%- 0%- A Particular COMT Gene and Psychosis 2.3% No Adolescent Marijuana Use (n=311) 5.5% Adolescent Marijuana Use (n=91)Two major automobile manufacturers have produced compact cars with engines of the same size. We are interested in determining whether or not there is a significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles. A random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance. The following data (in miles per gallon) show the results of the test. Assume the population of differences is normally distributed. Driver Manufacturer A Manufacturer B 1 36 30 2 31 31 3 30 28 4 30 27 5 29 27 6 33 30 7 35 25 8 29 31 The test statistic is 2.316. At ? = 0.10, the null hypothesis should be revised .should not be tested. should be rejected. should not be rejected.Use the data and table below to test the indicated claim about the means of two paired populations (matched pairs). Assume that the two samples are each simple random samples selected from normally distributed populations. Make sure you identify all values. The table below shows the blood glucose of 20 students before breakfast and two hours after breakfast, using a specific insulin dosing formula to cover carbohydrates. Is there compelling statistical evidence that the specific insulin dosing formula is effective in reducing blood glucose levels? Use a significance level of 0.05. We have the differences (gain or loss), but we still need to compute the mean, standard deviation, and know the sample size for the differences (use Excel or Sheets for this computation). Once those are found, we can apply methods that are used for a 1 sample t-test. Student Before Meal After Meal Difference 1 161 114 -47 2 196 88 -108 3 132 80 -52 4 175 96 -79 5 169 112 -57 6 138 137…