You have been asked to determine if two different production...

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 defined as μ1 and process 2 has a mean defined as μ2. The null and alternative hypotheses are H0: μ1 - μ2 ≤ 0 and H1: μ1 - μ2 > 0. The process variances are unknown but assumed to be equal. Using random samples of 49 observations from process 1 and 25 observations from process 2, the sample means are 59 and 48 for populations 1 and 2 respectively. Complete parts a through d: a. Can you reject the null hypothesis, using a probability of Type I error α = 0.05, if the sample standard deviation from process 1 is 31 and from process 2 is 28? The test statistic is t = _____ The critical value(s) is(are) _______________ (Round to three decimal places as needed. Use a comma to separate answers as needed.)

Transcript

00:01 In the given question we have a data for the parking tickets, parking tickets sold and we have a very large data.

00:14 So first of all we have to arrange our data, arrange the data in a sending order.

00:27 And after that we have to make a tallymark table to get the frequency of the data.

00:37 So then first of all we have to make our values for xi column and the values will be respectively 15 30 40 60 then we have 100 150 and 250 and 250 and then we have to count their respective frequencies fi for each column after that we will find our first observation which is ask into the question are value for the mean.

01:10 So here is the table.

01:12 I have created the table by using excel.

01:15 So these are the values of xi 15, 30, 40, 50, 60, 100, 150 and 250.

01:23 And these are the respective frequencies, 4, 50, 40s came for 34 times, then 2, 7, 2, 5 and 1.

01:35 And sum is here, sum of all frequencies f i is equal to one zero five as given into the question and then i have find it here x i into f i for each value and here we have our sum of f i x i which is equal to 4600440 so first part of the answer where we need to find the main so formula for mean is equal to bar x or we can take mu here is equal to summation of f i x i divided by summation of f i so here the value is 4 640 for all values of f i x i divided by 1045 so our value for main x bar will be equal to 44 .19047619.

02:35 This is the complete value and we can round off our mean value as 44 .19.

02:41 So here is the solution for the fourth part of the question.

02:45 Now we are done with the value of mean.

02:48 Answer for part a here.

02:52 Now let's move on to the part b.

02:54 In the part b, the question is asking for the sample standard deviation.

02:59 So formula for standard deviation is sigma is equal to square root of x minus mean x i minus mean to the whole square divided by frequency summation of fi so here you can see in the table i have created this particular column for all values of x minus x bar here which is represent mean and we have all the values and here the column is for x minus x bar to the whole square and we have find it the sum also.

03:41 So here when we find out our value has 5802 .62098 divided by 105 and we will get the square value of it so we will get our standard deviation for the given sample will be equal to 34 .0 .0...

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