6. Suppose we have a sample average X = 0.75 with standard error o, = 0.33. What is the 95% confidence interval for X (assuming we have a large n)? Would you reject the null hypothesis that Ho : µ = 0 for an alternative Ha : µ > 0?
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- Grace Floral Shop claims that their average daily earnings is $497. An auditor wants to determine whether this claim is true. The auditor randomly selected a sample of 100 days and found that the sample mean earnings was $495 with a sample standard deviation of 9.75. Calculate the 97% confidence interval for the population mean daily earning. Assist the auditor in conducting a hypothesis test, at the 3% level of significance, to determine whether the claim about their average daily earnings was overstated. State the null and the alternative hypothesis for this test. Using the p-value approach, state the decision rule for this Calculate the value of the test statistic for this test. Calculate the p-value for this test? State the conclusion of this test. Give reason for yourA statistics instructor is interested in the ability of students to assess the difficulty of a test they have taken. This test was taken by a large group of students, and the average score was 78.5. A random sample of eight students was asked to predict this average score. Their predictions were as follows:72 83 78 65 69 77 81 71Assuming a normal distribution, test the null hypothesis that the population mean prediction would be 78.5. Use a two-sided alternative and a 10% signifi- cance level.Given the following hypotheses: H0: μ ≤ 8 H1: μ > 8 A random sample of 10 observations is selected from a normal population. The sample mean was 11 and the sample standard deviation was 4.6. Using the 0.1 significance level: State the decision rule. (Round your answer to 3 decimal places.) Compute the value of the test statistic. (Negative answers should be indicated by a minus sign. Round your answer to 3 decimal places.) What is your decision regarding the null hypothesis?
- A sample of 42 observations is selected from a normal population. The sample mean is 41, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level. H0: μ = 43 H1: μ ≠ 43 Is this a one- or two-tailed test? multiple choice 1 One-tailed test Two-tailed test What is the decision rule? multiple choice 2 Reject H0 if −1.960 < z < 1.960 Reject H0 if z < −1.960 or z > 1.960 What is the value of the test statistic? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.) What is your decision regarding H0? multiple choice 3 Fail to reject H0 Reject H0 e-1. What is the p-value? (Round your z value to 2 decimal places and final answer to 4 decimal places.) e-2. Interpret the p-value? (Round your z value to 2 decimal places and final answer to 2 decimal places.)A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized here: Sample Size Sample Mean Population Standard Deviation Men 31 29 5 Women 36 34 10 At the 0.01 significance level, we ask if there is a difference in the mean number of times men and women send a Twitter message in a day. Assume that women are Population 1 and men are Population 2. What is the value of the test statistic for this hypothesis test? a. 2.907 b. 2.641 c. 2.815 d. 2.911What is meant by the assumption that the paired sample observations ofYi and Xi are independently and identically distributed? Why is this animportant assumption for ordinary least-squares estimation? When is thisassumption likely to be violated?
- Consider the following hypothesis test: H 0: 50 H a: > 50 A sample of 55 is used and the population standard deviation is 7. Use the critical value approach to state your conclusion for each of the following sample results. Use = .05. With = 52.5, what is the value of the test statistic (to 2 decimals)?Can it be concluded that the population mean is greater than 50?Select Yes No Item 2 With = 51, what is the value of the test statistic (to 2 decimals)?Can it be concluded that the population mean is greater than 50?Select Yes No Item 4 With = 51.8, what is the value of the test statistic (to 2 decimals)?Can it be concluded that the population mean is greater than 50?A hypothesis will be used to test that a population mean equals 9 against the alternative that the population mean is less than 9 with known variance . What is the critical value for the test statistic for the significance level of 0.025? Round your answer to two decimal places (e.g. 98.76).What is the value of the test statistic for a test with a null hypothesis that mu = 250, Xbar = 260 the standard deviation = 5 and n = 100?
- The null and alternate hypotheses are: H0 : μ1 = μ2 H1 : μ1 ≠ μ2 A random sample of 8 observations from one population revealed a sample mean of 23 and a sample standard deviation of 4.6. A random sample of 8 observations from another population revealed a sample mean of 27 and a sample standard deviation of 4.6. The population standard deviations are unknown but assumed to be equal. At the 0.01 significance level, is there a difference between the population means? a. State the decision rule. b. Compute the pooled estimate of the population variance. c. Compute the test statistic.ASSISTANCE REQUIRED FOR PART "e" i- vi ONLY, please. Also can you please show step by step how to get null and alternative in the hypothesis? A car company wants to know the monthly sales made in ($000), based on the brand of vehicle.The data collected was entered on a MINITAB spreadsheet for analysis. Exhibit II below was subsequently generated. Exhibit 2 Model N Mean Median Tri.Mean Std Dev S.E. Mean Hyundai 23 109 135 107.64 * 1.34 Toyota 27 165 124 143.65 9.5 ** a) Determine the values of * and **. b) Give the unbiased point estimate for the average monthly earning from Hyundai Vehicles.c) Give the unbiased point estimate for the variance of monthly earning from Hyundai Vehicles.d) Assuming normality, construct and interpret a 90% confidence interval for the average monthly earning from Toyota Vehicles. e) You are required to test at the 5% level of significance the hypothesis that the average monthly earnings on Hyundai Vehicles is equal to $110,000 versus the…1) A researcher estimates an AR(1) with an intercept and finds that the OLS estimate of β1 is 0.95, with a standard error of 0.02. Does a 95% confidence interval include β1=1? A.Yes, since the value of the t-statistic for the null hypothesis β1=1 is −2.50 and the 5% critical value of the augmented Dickey-Fuller statistic is −2.86, the null hypothesis is not rejected. Thus β1=1 is in the 95% confidence interval. B.No, the interval, calculated as β1±1.96SEβ1, is from 0.91 to 0.99. C.No, since the value of the t-statistic for the null hypothesis β1=1 at the 5% level is −2.50. D.No, because the critical value of the augmented Dickey-Fuller statistic at the 5% significance level is −2.86.