Froni the nformation given in attached, determine whether the difference between the variability of life of bulbs from each sample is significant.
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Froni the nformation given in attached, determine whether the difference between the variability of life of bulbs from each sample is significant.
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- The number of contaminating particles on a silicon waferprior to a certain rinsing process was determined for eachwafer in a sample of size 100, resulting in the followingfrequencies:Number of particles 0 1 2 3 4 5 6 7Frequency 1 2 3 12 11 15 18 10Number of particles 8 9 10 11 12 13 14Frequency 12 4 5 3 1 2 1a. What proportion of the sampled wafers had at leastone particle? At least five particles?b. What proportion of the sampled wafers had betweenfive and ten particles, inclusive? Strictly between fiveand ten particles?c. Draw a histogram using relative frequency on thevertical axis. How would you describe the shape of thehistogram?Two samples of rats are timed for their maze running time. One group is taking a drug and the other is not. The times are given in the following table: Rats with drug Rats without drug 15 12 13 12 10 11 11 13 9 6 11 Determine whether the use of the test drug results in a different maze running time. Use the level .05 level of significance.3) A firm in Lebanon has developed a chemical solution that can be added to car gasolinewhich they believe will increase the miles per gallon that cars will get. The owners areinterested in estimating the difference between mean mpg for cars using the chemicalsolution versus those that are not using the solution. The following data represent the mpgfor independent random samples of cars from each population.with Solution without Solution______________________________n1 = 36 n2 = 42 x1 = 25.45 x2 = 24.1 _______________________________Assume that the populations are normally distributed and the population standarddeviations are known to be σ1 = 3.95 (with solution) and σ2 = 3.09 (without solution).Given this data, can the owners believe that there is a difference between mean mpg forcars using the chemical solution versus those that are not using the solution? Test using analpha level equal to 0.05.4) Given the following null and alternative hypothesis:H0: σ 2 ≤ 52HA : σ 2 > 52and the…
- A critical dimension of the service quality of a call center is the wait time of a caller to get to a sales representative. Periodically, random samples of three customer calls are measured for time. The results of the last four samples are in the following table: Sample Time (Sec) 1 495 501 498 2 512 508 504 3 505 497 501 4 496 503 492 a. Assuming that management is willing to use three-sigma control limits, and using only the historical information contained in the four samples, show that the call center access time is in statistical control.b. Suppose that the standard deviation of the process distribution is 5.77. If the specifications for the access time are 500 ± 18 sec., is the process capable? Why or why not? Assume three-sigma performance is desired.A researcher obtains t(20) = 2.00 and MD = 9 for a repeated-measures study. If the researcher measures effect size using the percentage of variance accounted for, what value will be obtained for r2?To evaluate the effect of a treatment, a sample is obtained from a population with a mean of µ=20, and the treatment is administered to the individuals in the sample. After the treatment, the sample mean is found to be M=21.3 with a variance of s²=9. a. Assuming that the sample consists of n=16 individuals , use a two-tailed hypothesis test with α=.05 to determine whether the treatment effect is significant and compute both Cohen's d and r² to measure effect size. Are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with α=.05? b. Assuming that the sample consists of n=36 individuals, repeat the test and compute both measures of effect size. c. Comparing your answers for parts a and b, how does the size of the sample influence the outcome of a hypothesis test and measures of effect size?
- 1) A cement producer, manufactures and then fills 40kg-bags of powder cement on twodistinct production tracks located in separate suburbs. To determine whether differencesexist between the average fill rates for the two tracks, a random sample of 25 bags fromTrack 1 and a random sample of 16 bags from Track 2 were recently selected. Each bag’sweight was measured and the following information measures from the samples arereported:Production ProductionTrack 1 Track 2n1 = 25 n2 = 16x2 = 40.02 x1 = 39.87 s1 = 0.59 s2 = 0.88 Supervision believes that the fill rates of the two tracks are normally distributed with equalvariances.Construct a 95% confidence interval estimate of the true mean difference between the twotracks.--------------------------------------------------------------------------------------------------------------2) Two independent simple random samples were selected from two normallydistributed populations with unequal variances yielded the following information:Sample 1…31% of all pygmy softshell tortoises have stripes on their shells. A herpetologist in Cititon collects a sample of 28 pygmy softshell tortoises and finds that 8 of them have stripes on their shells. Is there enough evidence to conclude, at a significance of alpha = 0.05, that the proportion of pygmy softshell tortoises in Cititon with stripes on their shells is less than 31%? What is the claim? What is the null hypothesis? What is the alternative hypothesis? What is the test statistic? What is/are the critical value(s)? Do we reject the null hypothesis? What conclusion do we draw? What is the P-value for the problem above?Following is the rating of marketing aggressivity (X) and sales performance (Y) of 8 sales staffs in Glovis Co in the past year: Table Attached Question: What is the hypothesis of the study?
- which of the following individuals is likely to be excluded from a clinical trial? a-individual with other diseases besides the disease of interest b-an individual whose data is considered to be an outlier c-an individual of who is considered to be a minority d-an individual who will have difficulty complying trial protocols.Suppose a researcher is interested inthe effectiveness in a new childhood exercise program implemented in a SRS of schools across a particular county. In order to test the hypothesis that the new program decreases BMI (Kg/m2), the researcher takes a SRS of children from schools where the program is employed and a SRS from schools that do not employ the program and compares the results. Assume the following table represents the SRSs of students and their BMIs. Student intervention group BMI (kg/m2) Student control group BMI (kg/m2) A 18.6 A 21.6 B 18.2 B 18.9 C 19.5 C 19.4 D 18.9 D 22.6 E 24.1 F 23.6 A) Assuming that all the necessary conditions are met (normality, independence, etc.) carry out the appropriate statistical test to determine if the new exercise program is effective. Use an alpha level of 0.05. Do not assume equal variances.B) Construct a 95% confidence interval about your estimate for the average difference in BMI between the groups.An investigator hypothesizes that the improvement rate associated with a placebo is P1 = 0.45, and that the improvement rate associated with an active drug is P2 = 0.65. The plan is to perform a two-tailed test. Use SAS to complete each problem below. (a) If a significance level 0.01 and a power of 0.95 are desired, how large a sample per treatment must he study? (b) How large must the sample size be if the significance level is relaxed to 0.05 and the power to 0.85? (c) For this study, suppose that you have funds to recruit 130 patients per group. What is the power for a 5% level test for this sample size? First do the computation by hand and then use SAS to confirm.