Under which of the following conditions would you need to use the Fisher's exact test instead of the chi-square test?
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- Suppose that you want to perform a hypothesis test based on a simple random paired sample to compare the means of two populations and you know that the paired-difference variable has a symmetric distribution that is far from normal. a. Is use of the paired t-test acceptable if the sample size is small or moderate? Why or why not?b. Is use of the paired t-test acceptable if the sample size is large? Why or why not?c. Is use of the paired Wilcoxon signed-rank test acceptable? Why or why not?d. If both the paired t-test and the paired Wilcoxon signed-rank test are acceptable, which test is preferable? Explain your answer.If the sample data are in the critical region with α = 0.01 and Ho is rejected, then one could still reject Ho even if α were changed to 0.05. Is this statement True or False?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?A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. A recent sample of 1,000 adults showed 410 indicating that their financial security was more than fair. Suppose that just a year before, a sample of 1,200 adults showed 420 indicating that their financial security was more than fair. (a) State the hypotheses that can be used to test for a significant difference between the population proportions for the two years. (Let p1 = population proportion most recently saying financial security more than fair and p2 = population proportion from the year before saying financial security more than fair. Enter != for ≠ as needed.) H0: p1−p2=0 Ha: p1−p2!=0 (b) Conduct the hypothesis test and compute the p-value. At a 0.05 level of significance, what is your conclusion? Find the value of the test statistic. (Use p1 − p2. Round your answer to two decimal places.) Find the p-value.…
- A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. A recent sample of 1,000 adults showed 410 indicating that their financial security was more than fair. Suppose that just a year before, a sample of 1,200 adults showed 420 indicating that their financial security was more than fair. (a)State the hypotheses that can be used to test for a significant difference between the population proportions for the two years. (Let p1 = population proportion most recently saying financial security more than fair and p2 = population proportion from the year before saying financial security more than fair. Enter != for ≠ as needed.) H0: Ha: (b) Conduct the hypothesis test and compute the p-value. At a 0.05 level of significance, what is your conclusion? Find the value of the test statistic. (Use p1 − p2. Round your answer to two decimal places.) = Find the p-value. (Round your answer to…In a certain school district, it was observed that 29% of the students in the elementary schools were classified as only children (no siblings). However, in the special program for talented and gifted children, 78 out of 231 children are only children. The school district administrators want to know if the proportion of only children in the special program is significantly different from the proportion for the school district. Test at the a = 0.02 level of significance. Using the approximation for for the bimomial distribution (without the continuity correction), was in the test statistic for this sample based on the sample proportion? z = 3 decimal places P-value = 4 decimal placesIf the sample data are in the critical region with α = .01, then the same sample data would still be in the critical region if α were changed to .05. True False
- In a random sample of n=1000 families in the city of Portland, it is found that x=600families own at least two cars.(a) Find a 95% confidence interval for the actual proportion of families with at least twocars in this city. (b) If we want to claim with 95% confidence that our estimate of the percentage offamilies owning at least two cars in Portland is off the actual percentage by less than0.025, does the sampling provide sufficient supports for this claim? Why?The management of a supermarket wants to adopt a new promotional policy of giving free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditure for all customers at this supermarket will be normally distributed with mean 400 £ and a variance of 900 £2. 2) In a sample of 250, find the count that corresponds to the interquartile range. 3) Based on your answer in and without any calculation, if the mean changed to be 500 £, would the probability be the same?You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean de- fined as µ1 and process 2 has a mean defined as µ2.The null and alternative hypotheses are as follows:H0 :µ1 - µ2 ≤ 0H1 :µ1 - µ2 > 0The process variances are unknown but assumed to be equal. Using random samples of 25 observations from process 1 and 36 observations from process 2, the sample means are 56 and 50 for populations 1 and 2, respectively. Can you reject the null hypothesis using a probability of Type I error α = 0.05 in each case?a. The sample standard deviation from process 1 is 30 and from process 2 is 28.b. The sample standard deviation from process 1 is 22 and from process 2 is 33.c. The sample standard deviation from process 1 is 30 and from process 2 is 42.d. The sample standard deviation from process 1 is 15 and from process 2 is 36.