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- The burning rates of two different solid-fuel propellants used in air crew escape systems are being studied. A random sample of 15 first type propellants are tested resulting in a sample mean burning rate of 18 cm/s and sample standard deviation of 2.75 cm/s. Another sample of 15 second type propellants are tested resulting in a sample mean burning rate of 24 cm/s and sample standard deviation of 2.80 cm/s. Assume both populations are independent and normally distributed and have the equal but unknown variances. (a) Is there sufficient evidence to claim that the mean burning rate of the first type propellant is less than that of the second type propellant at α = 0.05? Use fixed significance level approach to answer this question. (b) Construct an appropriate confidence interval to answer question in part (a). (c) Without doing any calculation or looking up a table, can you figure out whether P-value is greater than 0.05? Why or why not?In attempting to improve student services, a college investigates its registration processand finds that for 12 randomly selected students, the mean registrationi timewas 73.2 minutes with a standard deviation of 14.2 minutes. Another collegei findsthat for 15 randomly selected students, the mean registration time was 42.3 minutes with a standard deviation of 9.8 minutes. At the 0.01 significance level, test the claim that the two samples came from populations with the same means. Assumeequal population variances.In attempting to improve student services, a college investigates its registration process and finds that for 12 randomly selected students, the mean registration time was 73.2 minutes with a standard deviation of 14.2 minutes. Another college finds that for 15 randomly selected students, the mean registration time was 42.3 minutes with a standard deviation of 9.8 minutes. At the 0.01 significance level, test the claim that the two samples came from populations with the same means. Assume equal population variances.
- A 30 month study is conducted to determine the difference in rates of accidents per month between two departments in an assembly plant. If a sample of 12 from the first department averaged 12.3 accidents per month with a standard deviation of 3.5, and a sample of 9 from the second department averaged 7.6 accidents per month with standard deviation of 3.4, find: The pooled variance estimator (sp2) (round off to three decimal places) is:The result of a sample study in a medium size college provided that 68 STEM major students average 13.9 math study hours with a standard deviation of 4.9 in a given month, while 54 students average 10.1 with a standard deviation of 6.7. Test at the 0.01 level of significance if the means of the two sample means are the same.A university research team was studying the relationship between idea generation by groups with and without a moderator. For a random sample of four groups with a moderator, the mean number of ideas generated per group was 78.0, and the standard deviation was 24.4. For a random sample of four groups without a moderator, the mean number of ideas generated was 63.5, and the standard deviation was 20.2. Test the assumption that the two population variances were equal against the alternative that the population variance is higher for groups with a moderator.
- In order to study the average number of continuous push-ups that his students can perform, a physical education teacher subjects 75 of them, chosen at random, to a test. The number of push-ups performed by each student, as well as their gender and whether or not they do sports outside school hours.The number of push-ups is known to be distributed according to a population variance norm 7.5.Can it be assumed considering a significance level of 5% that the mean number of push-ups performed by the students is 55?Make the respective graphMake the table with the classes and relative frequenciesA quality analyst conducts a small-scale study to compare the average capacity of two brands of AA batteries (A and B). A random sample of 11 batteries of Brand A has an average capacity of 851 mAh (milliampere-hours), and an independent random sample of 10 batteries of Brand B has an average capacity of 872 mAh. The sample standard deviations are 26.8 mAh and 31.9 mAh, respectively. It is assumed that battery capacity is normally distributed for both brands and the two distributions have the same variance. Find the pooled sample estimator of the true population variance. (Provide your answer as a number rounded to 2 decimal places).A quality analyst conducts a small-scale study to compare the average capacity of two brands of AA batteries (A and B). A random sample of 10 batteries of Brand A has an average capacity of 1065 mAh (milliampere-hours), and an independent random sample of 10 batteries of Brand B has an average capacity of 994 mAh. The sample standard deviations are 23.6 mAh and 38.0 mAh, respectively. It is assumed that battery capacity is normally distributed for both brands and the two distributions have the same variance. Find the upper limit of a 95% confidence interval for the difference between the population means. Form the confidence interval around a positive point estimate for the difference between the means. In order to obtain a positive point estimate, make sure you subtract the lower value from the higher value when calculating the difference between the sample means. (Provide your answer as a number rounded to the nearest integer.)