Factory A Factory B No. of bulbs in sample 100 200 Average Life 1100 900 Standard Deviation 240 220 From the above information, determine whether the difference between the variability of life of bulbs from each sample is significant. Use 1% level of significance.
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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…
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- 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.