(a) The first of two sub-groups has 100 items with mean 15 and standard deviation 3. the whole group has 250 items with mean 15.6 and standard deviation J13. 44, find the standard de- viation ofihe second sub-group.
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- A comparison is made between two bus lines to determine if arrival times of their regular buses from Denver to Durango are off schedule by the same amount of time. For 51 randomly selected runs, bus line A was observed to be off schedule an average time of 53 minutes, with standard deviation 15 minutes. For 60 randomly selected runs, bus line B was observed to be off schedule an average of 60 minutes, with standard deviation 11 minutes. Do the data indicate a significant difference in average off-schedule times? Use a 5% level of significance. What are we testing in this problem? difference of proportionsdifference of means single meanpaired differencesingle proportion (a) What is the level of significance?State the null and alternate hypotheses. H0: ?1 = ?2; H1: ?1 < ?2H0: ?1 = ?2; H1: ?1 ≠ ?2 H0: ?1 > ?2; H1: ?1 = ?2H0: ?1 = ?2; H1: ?1 > ?2 (b) What sampling distribution will you use? What assumptions are you making? The Student's t. We assume that both population…A new computer chip design(A) is being compared to the current design(B).Fifty independent chips of each design are tested for speed at performing a certain task. The new computer chip (A) performed the task in 481.2 ms, on average, with a sample standard deviation of 14.3 ms. The current computer chip (B) performed the task in 495.6 ms, on average, with a sample standard deviation of 16.4 ms. Can you conclude, at a 5% significance level, that chip A performs this task faster than chip B?The sociologist finds that for a certain population, the mean number of years of educations is 13.2 years witha standard deviation of 3.04 years. From a certain region, a random sample of 62 people is drawn from thispopulation and recorded a sample mean of 13.96 years. Test the claim that the mean number of years ofeducation is the same from the population with 0.05 level of significance.
- A sample of 45 adult men from Lahug showed that the mean time they spend working from home is 28.50 hours per week with a standard deviation of 4 hours. Another sample of 40 adult men from Pardo showed that the mean time spent by them working from home is 23.25 hours per week with a standard deviation of 5 hours. Using a 2.5% significance level, can you conclude that the mean time spent working from home by adult men in Lahug is greater than that for adult men in Pardo? Assume that the standard deviations for the two populations are equal.An elementary school class ran 1 mile with a mean of 11 minutes and a standard deviation of 3minutes. Rachel, a student in the class, ran 1 mile in 8 minutes. A junior high school class ran 1mile with a mean of 9 minutes and a standard deviation of 2 minutes. Kenji, a student in the class,ran 1 mile in 8.5 minutes. A high school class ran 1 mile with a mean of 7 minutes and a standarddeviation of 4 minutes. Nedda, a student in the class, ran 1 mile in 8 minutes. a. Why is Kenji considered a better runner than Nedda, even though Nedda ran faster than he? b. Who is the fastest runner with respect to his or her class? Explain whyA study of B.A. (Hons.) Economics examination results of 1000 students in 1990 gave the mean теаn grade as 78 and the standard deviation as 8.0. A similar study in 1995 revealed the mean grade of the group as 80 and the standard deviation as 7-6. In which year was there the greater (i) absolute dispersion, (ii) relative dispersion ? What can we say about the average performance of the students over time?
- Researchers interested in determining the relative effectiveness of two different drug treatments on people with a chronic illness established two independent test groups. The first group consisted of 15 people with the illness, and the second group consisted of 11 people with the illness. The first group received treatment 1 and had a mean time until remission of 187 days with a standard deviation of 6 days. The second group received treatment 2 and had a mean time until remission of 162 days with a standard deviation of 8 days. Assume that the populations of times until remission for each of the two treatments are normally distributed with equal variance. Construct a 90% confidence interval for the difference H₁-H₂ between the mean number of days before remission after treatment 1 (H₁) and the mean number of days before remission after treatment 2 (H₂). Then find the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three…A study of the wages of 100 persons grouped in class-intervals of Dollar 10-12, 12 14 ... etc. revealed the mean wage to dollar. 32.02 and its standard deviation as dollar. 13.18. Later, it was discovered that the wage of a labourer who was getting Dollar 57 was misread as 27. Calculate the correct mean and standard deviation?A particular IQ test is standardized to a Normal model, with a mean of 80 and a standard deviation of 8. A group of 8,000 people had participated in a study based on IQ. Using the Empirical rule determine about how many of them should have IQ scores more than 72?
- The lightbulbs in an industrial warehouse have been found to have a mean lifetime of 1030 hours, with a standard deviation of 90 hours. The warehouse manager has been approached by a representative of a company that makes a device intended to increase bulb life. Manager agrees to test the device by considering 40 bulbs equipped with the device and finds their mean life to be 1061.6 hours. Using level of significance of your choice can you conclude that the device was effective?If batteries have lives that are normally distribute with mean 2, 800 hours and standard deviation 400 hours, using the 68-95-99.7 rule to approximate the percentage of batteries having a life less than 3, 600 hours.A random sample of 46 adult coyotes in a region of northern Minnesota showed the average age to be x = 2.07 years, with sample standard deviation s = 0.88 years. However, it is thought that the overall population mean age of coyotes is ? = 1.75. Do the sample data indicate that coyotes in this region of northern Minnesota tend to live longer than the average of 1.75 years? Use ? = 0.01. (a) What is the level of significance?State the null and alternate hypotheses. H0: ? = 1.75 yr; H1: ? > 1.75 yrH0: ? > 1.75 yr; H1: ? = 1.75 yr H0: ? = 1.75 yr; H1: ? ≠ 1.75 yrH0: ? < 1.75 yr; H1: ? = 1.75 yrH0: ? = 1.75 yr; H1: ? < 1.75 yr (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since the sample size is large and ? is known.The standard normal, since the sample size is large and ? is unknown. The standard normal, since the sample size is large and ? is known.The Student's t, since the sample size is…