Consider the following hypothesis test h u20 h u20 a sample...

Name: consider the following hypothesis test h u20 h u20 a sample of 50 provided a sample mean of 194 the population standard deviation is 20 a compute the value of the test statistic to 2 decimal 79176
Uploaded: 2024-04-30T10:42:16-08:00
Duration: 4 min 45 s
Channel: Adi S
Description: consider the following hypothesis test h u20 h u20 a sample of 50 provided a sample mean of 194 the population standard deviation is 20 a compute the value of the test statistic to 2 decimal 79176

Consider the following hypothesis test: H: u>20 H: u<20 A sample of 50 provided a sample mean of 19.4 . The population standard deviation is 2.0. a. Compute the value of the test statistic (to 2 decimals). Enter negative value as negative number. b. What is thep -value (to 2 decimals)? c. Using a=.05 , can it be concluded that the population mean is less than ? - Select your answer - d. What is the rejection rule using the critical value? Use a=0.05 . Round your answer to three decimal places. Enter negative value as negative number. Reject H if is - Select your answer - . Using the critical value approach, can it be concluded that the population mean is less than 20? - Select your answer -

Transcript

00:01 So, let us start with the concept which we are going to use here for this question.

00:06 We have to use z -scope formula to find out the statistics that is x bar minus mu by sigma over under root of n, where sigma by under root of n representing the standard error that is sigma by under root of n.

00:20 So, according to question we are given that the sample size is n is equals to 50, sample sample mean 19 .6 and standard deviation 1 .4.

00:36 So in the a part we have to compute the value of tested statistics that is z.

00:42 So for that first of all we need the standard error which can be equals to sigma by and out of n that will be equals to 1 .4 by and out of 50 will comes out to 0 .197.

00:55 Now we can compute the z statistic which will be equals to x bar minus mu by sigma by delta of n.

01:04 So this should be equals to see 19 .6 minus of mu should be 20 divided by the standard error is 0 .1979 we have just found.

01:17 Why did we doing this because see we have given the null hypothesis set to be as mu greater than equals to 20 and alternative haptics is set for mu less than to 20 means we have to perform the left -tailed test so after dividing this you will get z statistic value as negative of 2 .02122 now let us try to find it out the z critical that is z of alphabet so this should be equals to zero now significance level is given 0 .05 so 0 .05 by 2 will become sort of z of 0 .025 so you will get it from the table as 1 .96 and now we will have to compute the p value which will be equals to p for z left tilde z less than 2 negative of 2 .0 or 2 1 2 2 from p value table you will get this p value as 0 .021 or 6.

02:28 So basically this is what the answer for a part of our question.

02:34 Now in similar way in the b part we will have to compute the p value.

02:39 So, this is what the p -value and answer for b part.

02:44 Now, in c, by using the significance level of alpha, we have to conclude the population mean is less than to 20 or not...

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