Let Y₁, Y2, Y3, Y4, Y5 and X₁, X2,..., X, be independent and normally distributed random samples from populations with means μ₁ = 2 and ₂ = 8 and variances ₁² = 5 and ₂² = k₁ respectively. Suppose that P(X-Y> 10) = 0.02275, find the value of σ₂² = k.
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- A university wants to investigate 'low-performance' modules - where low-performance is defined as a module with an average final mark lower than 50 in a given year. To test whether ECO242 is a 'low-performance' module, a researcher gathers data on final marks for 31 first ECO242 students from past years. If the mean and variance of this sample is estimated, respectively, as 48 and 38, test the hypothesis, at α=0.05, that the true mean is 50 against the hypothesis that it is less than 50. Q1: Is this an example of (two/left/right) tailed test?A university wants to investigate 'low-performance' modules - where low-performance is defined as a module with an average final mark lower than 50 in a given year. To test whether ECO242 is a 'low-performance' module, a researcher gathers data on final marks for 31 first ECO242 students from past years. If the mean and variance of this sample is estimated, respectively, as 48 and 38, test the hypothesis, at α=0.05, that the true mean is 50 against the hypothesis that it is less than 50. Q3: State the t-test statistic value and the critical value.A university wants to investigate 'low-performance' modules - where low-performance is defined as a module with an average final mark lower than 50 in a given year. To test whether ECO242 is a 'low-performance' module, a researcher gathers data on final marks for 31 first ECO242 students from past years. If the mean and variance of this sample is estimated, respectively, as 48 and 38, test the hypothesis, at α=0.05, that the true mean is 50 against the hypothesis that it is less than 50. Q2: What is the null and alternative hypothesis?
- Suppose that X1, ..., Xn are random variables such that the variance of each variable is 1 and the correlation between each pair of different variables is 1/4. Determine Var (X1 + ...+Xn).Suppose that 90% of Narnians are children, that Narnian children have normallydistributed BMIs with a mean of 25 kg/m2and variance of 64 (kg/m2) 2, and that Narnianadults have normally distributed BMIs with a mean of 30 kg/m2and variance of 100(kg/m2)2. WHO currently categorizes BMIs greater than 30 as obese.a. What is the prevalence of obesity among Narnian children?b. What is the prevalence of obesity among Narnian adults?c. What is the overall prevalence of obesity among Narnians?d. Are age and obesity statistically independent in Narnia?e. What proportion of Narnians are obese children?f. What proportion of obese Narnians are children?Suppose that 90% of Narnians are children, that Narnian children have normally distributed BMIs with a mean of 25 kg/m^2 and variance of 64 (kg/m^2)^2 , and that Narnian adults have normally distributed BMIs with a mean of 30 kg/m^2 and variance of 100 (kg/m^2)^2 . WHO currently categorizes BMIs greater than 30 as obese. a. What is the prevalence of obesity among Narnian children? b. What is the prevalence of obesity among Narnian adults? c. What is the overall prevalence of obesity among Narnians? d. Are age and obesity statistically independent in Narnia? e. What proportion of Narnians are obese children? f. What proportion of obese Narnians are children?
- A survey of go randomly selected hotels in each city found that the average hotel room rate in New Delhi is$88.42 and the average room rate in Mumbai is $80.61, with standard deviations of, in New delhi, $5.62 and,in Mumbai, $4.83. Assume that room rates are normally distributed in each city.a. Test at o.05 level of significance whether the two population variances differ.b. Based on your results of part a, use the appropriate case to test whether average room ratesdiffer at a = 0.05c. Construct a 95% confidence interval to estimate the difference in the two population means.d. Explain how the 95% confidence interval could be used to test the hypotheses in part b at a = 05, andcome to the same conclusion.A random sample of size n = 12 from a normal pop-ulation has the mean x = 27.8 and the variance s2 = 3.24. If we base our decision on the statistic of Theorem 13, canwe say that the given information supports the claim thatthe mean of the population is μ = 28.5?The following table shows the results of two random samples that measured the average number of minutesper charge for AA Lithium-ion (Li-ion) rechargeable batteries versus Nickel-Metal Hydride (NiMH)rechargeable batteries. Perform a hypothesis test using α =0.05 to determine if the average number ofminutes per charge for Li-ion batteries last longer than NiMH batteries. Assume the population variances forthe number of minutes per charge are unequal.Li-ion NiMH110 8798. 9290 9087. 8992 89101 8898 8788 9187 9299 86100. 88103 9089 92105 90909781 1)State the hypotheses. 2) Compute the test statistic and Compute the p-value. 3) Make the decision and Summarize the results.
- One sample with n =8 has a S2 = 6 and a second sample n = 8 scores has a S2 = 10. If the pooled variance is computed for these two samples, then the value obtained will beA 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.Suppose that you are given two random variables x and y and you take measurements and obtain x1 = 2.3%, x2 = −7.6%, x3 = 0.1% andy1 =60, y2 =120, y3 =80. Findthelineofbestfity=α+βx. Calculate the correlation coefficient r and perform a left-tailed hypothesis test for r with significance level 10%. Based on this test, should we use this line to find the value of y when x = .5%