13. A random sample of 200 observations indicate a sample mean of 4117 with a stand of 300. Test the hypothesis that the mean is greater than 4100 at a = 0.01. OC
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- Dr. Chapman conducted an experiment in which participants watched paint dry for 30 minutes twice, once being paid $1 and once being paid $30. When comparing the samples, he calculated t = 3.57. He assumed α = .01 with df = 5, so the tcv = ±4.032. Because the calculated value was: A. greater than the critical value, Dr. Chapman can reject the null hypothesis. B. greater than the critical value, Dr. Chapman failed to reject the null hypothesis. C. less than the critical value, Dr. Chapman failed to reject the null hypothesis. D. less than the critical value, Dr. Chapman can reject the null hypothesis.A random sample of 50 students was asked to estimate how much money they spent on textbooks in a year. The sample skewness of these amounts was found to be 0.83 and the sample kurtosis was 3.98. Test at the 10% level the null hypothesis that the population dis- tribution of amounts spent is normal.Suppose a linear model y=β0+β1xy=β0+β1x is fit to a sample data set, and a test of the null hypothesis H0:β1=0H0:β1=0 against an alternative hypothesis HA:β1≠0HA:β1≠0 is performed; a PP-value of 0.4203 is obtained. Which of the following scatter plots depicts the data set on which this model was fit and the hypothesis test was performed?
- 1)A new starch polymer foam with high shock absorbent properties is expected to perform better thanthe old foam which can withstand a maximum impact of 1.56 Joule (J). A simple destructive testto quantify shock absorption ability of the new foam is conducted. Table 5 shows the impact energyabsorbed (in J) that the new foam can withstand for each test. Table 51.61 1.5 1.65 1.7 1.4 1.59 1.65 1.5 Does the recorded data suggests that the new foam performs better than the old foam? Use 2.5%level of significance. 2) A number of 28 university students who smokes completed a questionnaire inquiring their smokinghistory and behavior. The result shows that the average smoking initiation age of this group is 21.6years with a variance of 18.49. Based on past record, the smoking initiation age of universitystudent has a mean of 20.74 years with a standard deviation of 5.1 years. Conduct a necessaryanalysis to determine if the smoking initiation age remain the same as the previous record.…The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO2 in a sample is normally distributed with ? = 0.32 and that x = 5.21. (Use ? = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5?State the appropriate null and alternative hypotheses. H0: ? = 5.5Ha: ? ≠ 5.5H0: ? = 5.5Ha: ? ≥ 5.5 H0: ? = 5.5Ha: ? < 5.5H0: ? = 5.5Ha: ? > 5.5 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average percentage differs from the desired percentage.Reject the null hypothesis. There is sufficient evidence…1. What does it imply if if more values are concentrated above the mean? (Skewness) And would the value of skewness be less than, greater than, or equal to 0? 2. In case the data is highly skewed, can we still rely on the kurtosis coefficient? Why or why not? 3. Can the z-score be a real measure of dispersion?
- Stock y has a beta of 1.2 and an expected return of 11.5. Stock z has a beta of .80 and an expected return of 8.5 percentAssume X_1, X_2, .....X_n are random samples from X~Exponential(θ).1) Find the MLE estimator of θ .If the df value for a two tailed test with alpha =0.05 were to increase from df=5 to df=22,what would happen to the critical values for t?
- A dietitian wishes to see if a person’s cholesterol level will be changed if the diet is supplemented by a certain mineral. Four subjects were pre-tested, and they took the mineral supplement for a 6-week period. The results are shown in the table. Is there sufficient evidence to conclude that the population mean of cholesterol levels has been changed after six weeks at α=0.2α=0.2? Assume that the differences are from an approximately normally distributed population. Subject Cholestrol Level (mg/dl) Cholestrol Level after 6 Weeks (mg/dl) dd ¯dd¯ (d−¯d)2(d-d¯)2 1 206 217 11 2 219 184 -35 3 202 204 2 4 213 205 -8 Total -30 a) Calculate the mean, the sum of the squared deviation from the mean, and the standard deviation of differences. Do not include the unit for each answer: ¯d=d¯= (do not round) ∑(d−¯d)2=∑(d-d¯)2= (do not round) sd=sd= (rounded to one decimal place) b) Perform the hypothesis test in the following steps: Step 1.…Researchers interested in lead exposure due to car exhaust sampled the blood of 52 police officers subjected to constant inhalation of automobile exhaust fumes while working traffic enforcement in a primarily urban environment. The blood samples of these officers had an average lead concentration of 124.32 µg/l and a SD of 37.74 µg/l; a previous study of individuals from a nearby suburb, with no history of exposure, found an average blood level concentration of 35 µg/l. Based on your preceding result, without performing a calculation, would a 99% confidence interval for the average blood concentration level of police officers contain 35 µg/l? Based on your preceding result, without performing a calculation, would a 99% confidence interval for this difference contain 0? Explain why or why not.In a test of H0: µ=75 against HA: µ<75, a sample of size 450 produces Z = -1.19 for the value of the test statistic. Thus the p-value is approximately equal to: