A sample mean sample size and sample standard deviation are...

A sample mean, sample size, and sample standard deviation are provided below. Use the one-mean t-test to perform the required hypothesis test at the 1% significance level. x = 26, s = 4, n = 24, H0: μ = 25, Ha: μ ≠ 25 The test statistic is t = _____. (Round to two decimal places as needed.) Identify the critical value(s). Select the correct choice below and fill in the answer box within your choice. (Round to three decimal places as needed.) A. The critical values are ±tα/2 = ±_____ B. The critical value is tα = ____ C. The critical value is -tα = _______ (Reject/Do not reject) the null hypothesis. The data (provide/do not provide) sufficient evidence to conclude that the mean is (less than 25/not equal to 25/equal to 25/greater than 25).

Transcript

00:01 So our question says a sample mean sample size and the sample standard deviation are provided below using, use the one mean t test to perform the required hypothesis test at 1 % level of significance.

00:11 We have the sample mean to be caused to 26.

00:13 We have the sample standard division to be cost to 4.

00:16 We have the sample size to be caused to 24.

00:19 We're also given the value of the null and alternative hypothesis.

00:23 So let's extract out the details.

00:25 The sample mean x by is equals to 24.

00:27 The sample standard vision s is equal to four at the sample size n we have that to be equals to 24 okay this is actually 26 please pardon me so we have the null hypothesis h not to be based on the fact that m is equal to 25 and the alternative hypothesis is that m is not equals to 25 so the first step is the questions we should get the test statistics so our test statistics is a t test and we have that t so question one t is equal to x bar minus me divided by s divided by the square root of n x by in this case is 26 minus our mu is 25 divided by our s is 4 the value by the scourts of 24 so we have this to be 1 divided by so 4 divided by square of 24 we have that to be 0 .8165 and when we do the mat one divided by square out of 8165 sorry 1 devere by 0 .8165 and that is 1.

01:33 1 .2 so our question simply leave our decimal place in two decimal place our test statistics in two decimal place rather so we have 1 .02 the second question say we should get the critical value and round it to 3 decimal place so to get the critical value we need to know the direction of our test and from these we can see that our test is a two -tailed test so our test is two -tailed we also need the level of significance and according to our question the level of significance alpha is 0 .01 so since this is a t -test the degree of freedom is going to be the sample size minus one and that's 24 minus 1 which is got 23 so these are the details we need to get our critical value i'll be using my calculator so we have a t student our test is two -tailed the girl freedom is 23 and our level of significance is a 0 .01 as you can see the critical value is 2 .873 cv is a plus or minus 2 .8073.

02:43 So the third question says that so let's make sufficient evidence sorry let's make a decision rather...

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