Number of mistakes found native english speaker 0 1 3 0 0 1...

Number of "mistakes" found "Native English Speaker" 0 1 3 0 0 1 0 0 0 2 1 2 0 0 3 2 0 0 2 0 "Non-native English speaker" 2 1 5 0 1 4 8 7 6 0 1 0 1 4 7 4 2 1 4 5 Do these data provide convincing evidence that readers are more likely to incorrectly identify errors in writing if they think the author's native language is not English? Support your conclusions with an appropriate statistical test.

Transcript

00:01 Hello, let's have a look on the questions.

00:01 This is the data given to us for non -native english speakers and the native english speakers.

00:07 Now, for the a part, we need to find out the hypothesis.

00:11 So, hypothesis here would be, we have null and alternating hypothesis, null hypothesis denoted by h0, that is, mu d is equal to 0, which means that is mu 1, that is the difference of means.

00:26 So, mu 1 minus mu 2 is equal to 0.

00:29 Next, we have the alternating hypothesis h1, which means mu d is greater than 0, that is, mu 1 is greater than mu 2.

00:40 So, these are the null and alternating hypothesis in this question.

00:44 Now, for the b part, we need to find out the p value, find p value.

00:51 But in order to find out the p value, first we need to find out the t statistics, then we can easily find out the value of p.

00:58 So, in this case, t will be equal to d bar divided by standard deviation divided by under root of n.

01:10 Now, we need to know these values in order to find out the value of t.

01:14 So, here d bar is given by 1 divided by n summation of di.

01:21 So, we can easily calculate this value, summation of di using the excel because we have all the values of non -native english speakers and native english speakers.

01:31 So, we can minus 0 from 2, 1 from 1, 3 from 5, then we can add the sum.

01:37 So, this will be equal to 1 divided by 2 multiplied by minus of 46, which is equal to minus of 2 .3...

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