If, in a sample of n=30 selected from a normal​ population, X=58 and S=12​, what is your statistical decision if the level of​ significance, α​, is 0.05​, the null​ hypothesis, H0​, is μ=50, and the alternative​ hypothesis, H1, is μ≠50? Click here to view page 1 of the table of the critical values of t. LOADING... Click here to view page 2 of the table of the critical values of t. LOADING...       Question content area bottom Part 1 Determine the critical​ value(s).   The critical​ value(s) is(are) enter your response here

You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05.      Ho:μ=68.1Ho:μ=68.1      Ha:μ<68.1Ha:μ<68.1You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=81n=81 with mean M=59.2M=59.2 and a standard deviation of SD=20.5SD=20.5.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic =Steps on TI-84????What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = steps on TI-84???The p-value is...??? less than (or equal to) αα greater than αα This test statistic leads to a decision to...?? reject the null accept the null fail to reject the null As such, the final conclusion is that...???? There is sufficient evidence to warrant rejection of the claim that the population mean is less than 68.1. There is not sufficient evidence to warrant rejection of the claim that the population mean is…

You wish to test the following claim (HaHa) at a significance level of α=0.05α=0.05.      Ho:μ=66.6Ho:μ=66.6       Ha:μ≠66.6Ha:μ≠66.6You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=19 with mean ¯x=74.3 and a standard deviation of s=11.5.What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value =

You wish to test the following claim (H1H1) at a significance level of α=0.005.      Ho:μ1=μ2      H1:μ1≠μ2You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size n1=17n1=17 with a mean of M1=52.8M1=52.8 and a standard deviation of SD1=9.4SD1=9.4 from the first population. You obtain a sample of size n2=14n2=14 with a mean of M2=47.4M2=47.4 and a standard deviation of SD2=10.5SD2=10.5 from the second population. What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to...  reject the null accept the null fail to reject the null As such, the final…

You wish to test the following claim (Ha) at a significance level of α=0.10.       Ho:μ1=μ2       Ha:μ1<μ2 You obtain a sample of size n1=21 with a mean of M1=72.5 and a standard deviation of SD1=18.7 from the first population. You obtain a sample of size n2=22 with a mean of M2=76.2 and a standard deviation of SD2=15.8 from the second population.  Use the Theory-based inference applet to conduct the test of significance. (a)  What is the t-score for this sample?       t-score =   (Round to 2 decimal places.)  (b)  What is the p-value for this sample?      p-value =   (Round to 4 decimal places.) (c)  The p-value is... less than (or equal to) α   greater than α     (d)  This p-value leads to a decision to... strong evidence to support the alternative accept the null null is plausible   (e)  As such, the final conclusion is that... We conclude that μ1<μ2 . We conclude that μ1=μ2 . We have statistically significant evidence to support the claim that μ1<μ2 ..…

Suppose there is a claim that a certain population has a mean, u, that is different than 5. You want to test this claim. To do so, you collect a large random sample from the population and perform a hypothesis test at the 0.05 level of significance. To start this test, you write the null hypothesis H. and the alternative hypothesis H₁ as follows. H₁ H=5 H₁: μ = 5 Suppose you also know the following information. The critical values are -1.960 and 1.960 (rounded to 3 decimal places). The value of the test statistic is 1.495 (rounded to 3 decimal places). (a) Complete the steps below to show the rejection region(s) and the value of the test statistic for this test. Standard Normal Distribution Step 1: Select one-tailed or two-tailed. O One-tailed O Two-tailed Step 2: Enter the critical value(s). (Round to 3 decimal places.) Step 3: Enter the test statistic. (Round to 3 decimal places.) (b) Based on your answer to part (a), choose the correct statement. O The value of the test statistic…

You wish to test the following claim (HaHa) at a significance level of α=0.01α=0.01.      Ho:μ=73.1Ho:μ=73.1      Ha:μ>73.1Ha:μ>73.1You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=223n=223 with mean M=74M=74 and a standard deviation of SD=5.2SD=5.2.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population means is greater than 73.1. There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 73.1. The sample data support…

The dataset below that contains information on fuel efficiency (in miles/gallon) from random samples of cars with manual and automatic transmissions as well as cars with other transmissions. Do these data provide strong evidence of a difference between the average fuel efficiency of cars with manual and automatic transmissions in terms of their average citymileage? 1. Set up the null and alternative hypotheses.2. Compute the test statistic.3. State the p-value for the test. State the decision and conclusion of the test in context. Feel free to use excel, Rstudio, or any other methods to answer the Question! Thanks Auto Manual 77 22 126 30 52 28 62 26 62 29 106 20 27 27 28 22 24 26 26 26 30 26 21 23 21 28 23 29 25 25 20 25 20 22 18 17 17 27 14 25 15 19 18 27 17 30 14 23 18 24 17 23 14 22 15 23 18 24 17 27 14 23 19 22 17 25 17 19 14 26 16 21 16 23 14 18 17 18 17 18 14 18 16 19 16 19 14 21 18 18…

You wish to test the following claim (H1H1) at a significance level of α=0.10α=0.10.      H0:μ=51.8      H1:μ<51.8You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=19n=19 with mean ¯x=42.4x¯=42.4 and a standard deviation of s=13.2s=13.2.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = ____________What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = __________The p-value is... less than (or equal to) αα or greater than αα This test statistic leads to a decision to... reject the null or accept the null or fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is less than 51.8. or There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 51.8. or The sample…

You wish to test the following claim (HaHa) at a significance level of α=0.01α=0.01.      Ho:μ1=μ2      Ha:μ1≠μ2You believe both populations are normally distributed, but you do not know the standard deviations for either. However, assume that the variances of the two populations are equal. You obtain a sample of size n1=20 with a mean of ¯x1=55.2 and a standard deviation of SD1=11.3SD1=11.3 from the first population. You obtain a sample of size n2=18 with a mean of ¯x2=48.3 and a standard deviation of SD2=7.2 from the second population.What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic =  What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to…