2. A professor claims that the mean final mark for STAT1P98...

2. A professor claims that the mean final mark for STAT1P98 is greater than 65. A sample of 35 students shows the sample mean is 67 with standard deviation 15. Test the professor's claim using a 0.05 significance level. a) State the null and alternative hypotheses. b) Calculate the test statistic (round it to 3 decimal places). c) Find the P-value (round it to 3 decimal places). d) Make a conclusion based on your answers in parts b) and c). e) Explain what would constitute a Type I error in this context. f) Explain what would constitute a Type II error in this context.

Transcript

00:01 Once again, welcome to a new problem.

00:04 This time we're dealing with hypothesis testing.

00:08 So we're dealing with hypothesis testing and when it comes to hypothesis testing, we have hypothesis testing for means under one sample t test.

00:21 So when you look at one sample t test, you're going to have the t test statistic is going to be t -e -q.

00:31 Equals to x bar minus mu not all over s over radical n.

00:36 Mu not is the hypothesized population mean.

00:50 So mu not is the hypothesized population mean.

00:54 Small n happens to be the sample size.

01:01 That's small n and s is the sample standard deviations.

01:10 So r s is the sample standard deviation.

01:17 X bar is the sample mean.

01:26 And then we have type 1 error.

01:30 So whenever type 1 error usually is alpha, when you reject a true null hypothesis.

01:43 And then of course type 2 error is when you fail to reject a false now hypothesis.

02:03 So we're looking at a problem where there's a final score in our statistics test, and there's a claim that this score is greater than 65.

02:16 We have a sample of 35 students, and the average performance for this sample is 67.

02:26 But the sample standard deviation is 15 and we want to test at an alpha level of 0 .05.

02:34 The first thing is to determine the now and alternative hypothesis.

02:39 So in part a, the now hypothesis, is that the mean is equivalent to 67...

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