Now let's look at the theoretical distribution: X f= σ= Q1 = U(0, 1)
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- Records for the last 15 years have shown that the average rainfall in a certain region of the country, for the month of March, to be 1.20 inches, with s = 0.45 inches. A second region had an average rainfall of 1.35 inches, with s = 0.54. estimate the difference of the true average rainfalls in those two regions as a 95% C.I. with the assumption of normal populations and unequal variances.The average number of pounds of sliced ham ordered per customer at the deli where Dennis used to work was 1.4, but at his new job, the average of the 32 people who have ordered ham so far is 1.5 pounds, with a standard deviation of 0.3 pounds. a) Write the null and alternative hypotheses to test if the average amount of ham bought is higher at the new store. H0:μ= H1:μ> b) For α=0.025, find the rejection region in terms of z. [Write your answer with 2 decimal places.] R:z≥ c) What test statistic corresponds to an x¯ of 1.5 pounds? [Round your answer to 2 decimal places.] z= d) Should you reject the null hypothesis?Based on sample data, newborn males have weights with a mean of3250.3g and a standard deviation of 726.3g. Newborn females have weights with a mean of 3061.3g and a standard deviation of 546.4g. Who has the weight that is more extreme relative to the group from which they came: a male who weighs 1600g or a female who weighs 1600g? Since the z score for the male is z= ?
- Which of the following can cause the usual OLS t statistics to be invalid (that is, not to have t distributions under H0)?(i) Heteroskedasticity.(ii) A sample correlation coefficient of .95 between two independent variables that are in the model.(iii) Omitting an important explanatory variable.Sketch the normal curve having the parameters a. µ = -1 and σ = 2.b. µ = 3 and σ = 2.c. µ = -1 and σ = 0.5.Assume the samples are random and independent and the populations are normally distributed. A marine biologist claims that the mean fork length of yellowfin tuna is different in two zones in the eastern tropical pacific ocean. A sample of 26 yellowfin tuna collected in zone A has a mean fork length of 76.2 centimeters and a standard deviation of 16.5 centimeters. A sample of 31 yellowfin tuna collected in zone B has a mean fork length of 80.8 centimeters. and a standard deviation of 23.4 centimeters. At alpha=0.01, can you support the marine biologist's claim? Assume the population variance are equal. Also, what will be your conclusion
- Two competing internet routers, A and B, are being compared for the transmission speeds they can achieve for a random selection of transmitted files. The company which produces router A claims that its transmission speed exceeds that of router B. To compare, 1000 randomly selected file transmissions are monitored for each router. The sample mean and sample standard deviation of the transmission speed for router A was determined to be 10.04 and 0.987 GB/sec, respectively, while the same parameters for router B were 8.972 and 1.032 GB/sec, respectively. a) Is it reasonable to assume that the true standard deviations are known? Why or why not? b) Construct a 95% confidence interval on the mean transmission speed for router A. c) Construct a 95% confidence interval on the mean transmission speed for router B. d) By constructing a 95% confidence interval on the difference between the means, would you say that the claim made by the company producing router A is reasonable?The standard deviation of the measurements made by a special thermocouple is assumed to be 0.005 ° C.If the standard deviation of a sample of 45 thermocouples is 0.01, perform a hypothesis test with alpha = 0.01Suppose 10% of new scooters will require warranty service within the first months of its sale. A scooter manufacturing company sells 1000 scooters in a month. (i) Calculate the mean and standard deviation of scooters that require warranty service. (ii) Calculate the moment coefficient of skewness and Kurtosis of the distribution.
- If X follows a gamma distribution with a mean of 12 and a standard deviation of 6 then the parameter:A park ranger is searching for bears in a region of the park where on average there are 5 bears per square mile. The bears are solitary independent creatures, so it is reasonable to assume that the numbers of bears in disjoint regions are independent unknowns and that the number expected in any region is proportional to the area of the region. The ranger can also assume that in a very tiny region, say a square inch, it is impossible to find more than one bear. What is the standard deviation in area (in square miles) he has to search in order to find 16 bears?Based on sample data, newborn males have weights with a mean of 3284.4 g and a standard deviation of 877.9 g. Newborn females have weights with a mean of 3004.9 g and a standard deviation of 585.1g. Who has the weight that is more extreme relative to the group from which they came: a male who weighs 500 g or a female who weighs 1500g? Since the Z score for the male is z=____ and the z score for the female is z=____, the _____ has the weight that is more extreme