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- Entry to a cerain university is determined by a national test. The scores on this test are normally distrubuted with a mean of 500 and a standard deviation of 100. Tom wants to be admitted to this university and he knows that he must score better than at least 70% of the students who took the test. Tom takes the test and scores 562. Will he be admitted to this university? Sketch the region in question. Write a sentence describing what your answer represents about the problems specifics.Two data sets are being compared. One data set is skewed left, and the minimum value is an outlier. Another data set is symmetric about its peak about the center of the distribution with no outliers. Explain whether the mean and standard deviation should be used to compare the measures of center and measures of spread. The mean and standard deviation should not be used because one of the distributions is skewed left and has an outlier. The mean and the standard deviation should be used because one of the distributions is symmetric with no outliers. The mean and the standard deviation should be used because the mean and the standard deviation are not affected by outliers. The mean and standard deviation should not be used because both of the distributions are skewed left, and both data sets have at least one outlier.Suppose a test is given to 20 randomly selected college freshmen in Ohio. The sample average score on the test is 12 points and the sample standard deviation is 4 points. Suppose the same test is given to 16 randomly selected college freshmen in Iowa. The sample average score on the test is 8 points and the sample standard deviation is 3 points. We want to test whether there is a significant difference in scores of college freshmen in Ohio versus Iowa. What is the point estimate for the difference in population means, where difference is defined as (Ohio minus Iowa)?
- the mean lung capacity for nonsmoking males in the population aged 50 is 2.2 liters. an investigator wants to examine if the mean lung capacity are significantly diffrent among former smokers of similar background(i.e, males aged 50 who smoked in the past and are not currently smoker). a random sample of 28 former smokers is selected. their lung capacity have a mean of 2.0 liters with a standard devision of 0.41 liters. calculate the appropirate test at the 1% level of significance. decide on a 1- tail or 2- tail test based on the goals of the research. the value of the calculated test statistic= the critical value= regarding the null hypothesisBefore every flight, the pilot must verify that the total weight of the load is less than the maximum allowable load for the aircraft. The aircraft can carry 40 passengers, and a flight has fuel and baggage that allows for a total passenger load of 6,250 lb. The pilot sees that the plane is full and all passengers are men. The aircraft will be overloaded if the mean weight of the passengers is greater than 6,250 lb / 40 = 163 lb. What is the possiblity that the aircraft is overloaded? Should the pilot take any action to correct an overloaded aircraft? Assume that the weights of men are normally distributed with a mean of 177.3 lb and a standard deviation of 39.3 The probability is approximatelyTimes for a surgical produce are normally distributed. There are two methods. Method A has a mean of 31 minutes and a standard deviation of 3 minutes while method B has a mean of 35 and a standard deviation of 1.5 minutes. Which procedure is preferred if the procedure must be completed within 30 minutes method A or B? which procedure is preferred if the procedure must be completed within 39.5 minutes method B or either method? which produce is preferred if the procedure must be completed within 39 minutes method B or either method?
- A sample of 20 from a population produced a mean of 66.0 and a standard deviation of 10.0. A sample of 25 from another population produced a mean of 58.6 and a standard deviation of 13.0. Assume that the two populations are normally distributed and the standard deviations of the two populations are equal. The null hypothesis is that the two population means are equal, while the alternative hypothesis is that the two population means are different. The significance level is 5%. Directions: • Label your answers with the correct statistical symbols. 3.2. By hand, what is the standard deviation of the sampling distribution of the difference between the means of these two samples, rounded to three decimal places? 3.3. What is/are the critical value(s) for the hypothesis test? 3.4. By hand, derive the corresponding 95% confidence interval for the difference between the means of these two populations, rounded to three decimal places. 3.5. What is the value of the test statistic rounded to…A medical researcher administers a new medication to a random sample of 70 flu sufferers, and she administers a placebo to another random sample of 50 flu sufferers. (She chooses the two samples so that their characteristics, such as age, are as similar as possible.) For each group, she monitors the number of days until the sufferers’ symptoms have disappeared. The sample mean and sample standard deviation for the first sample are 9.72 days and 2.31 days, respectively. These quantities for the second sample are 13.23 days and 3.45 days. The endpoints of a 90% confidence interval for the mean difference (placebo minus new medication) are closest to which of the following? a. 2.49 days to 4.53 days b. 2.59 days to 4.43 days c. 2.16 days to 4.86 days d. 2.66 days to 4.36 daysChebyshev's theorem states that for any set of numbers, the fraction that will lie within K standard deviations of the mean is at least 1-1/k^2. Use this theorem to find the fraction of all the numbers of a data set that must lie within 3 standard deviations from the mean. At least____of all numbers must lie within 3 standard deviations from the mean. ( Type an integer or a fraction)