5. Researchers claim that the average age at which children...

5. Researchers claim that the average age at which children start walking is 12.5 months. A child psychologist wanted to study if this claim was true. She took a random sample of 18 children and found that the mean age at which these children started walking was 12.1 months with a standard deviation of 1.5 months. If it is known that the ages at which all children start walking are approximately normally distributed with a population standard deviation of 0.80 months, does our sample data suggest that the true average age at which all children start walking is less than 12.5 months? Conduct this hypothesis test using a 1% level of significance. a. Identify the null and alternative hypotheses, writing them out using the symbols we used in class. b. State the level of significance. c. Calculate the test statistic, being sure to indicate if it is a z-score or a t-score. d. Find the critical number(s) OR calculate the p-value. e. State your decision to either reject the null hypothesis or fail to reject the null hypothesis. f. Restate the decision in the context of the problem in clear, plain English.

Transcript

00:01 So we're looking at some questions here, and they're kind of theoretical questions, and this is important when we're doing our analysis.

00:07 So we're told in this first one, a randomized experimental study was conducted to evaluate the effectiveness of a new vaccine, and 500 children were randomly assigned to the new rolled vaccine, and children who were followed for two years to monitor the incidence of this disease after they got the vaccine.

00:25 At the end of the study, the risk ratio for developing this disease, pertussis, was 0 .5 among the children who received the new vaccine compared to children who received the old vaccine.

00:34 So the risk ratio is less than one.

00:36 That's good to know.

00:37 It's an important thing to note.

00:38 And there was a 95 % confidence interval for this relative risk, was 0 .02 to 0 .08, and the p -value was here, 0 .01.

00:46 The question is, which of the following is the correct interpretation of the p -value of this thing? so the way we interpret a p -value, it's the probability, this is a probability statement, it's the probability of seeing the result we observed given the null hypothesis is true, which is right here.

01:02 Given that the null hypothesis is true, there's a 1 % probability of observing these or more extreme results.

01:07 This is our, that's how we interpret the p -value.

01:09 It's a probability statement.

01:14 This, i will say, this is a true, a correct interpretation of the confidence interval, that you're confident that the true relative risk lies in the interval 0 .2 to 0 .8, but the question is about the probability statement.

01:29 And in fact, for a, is the correct interpretation of that risk ratio too.

01:33 So it's kind of really focusing on the p -value.

01:36 All right, next question.

01:38 After we establish the null and alternative hypotheses and then calculate the probability statistic to determine if the study results were compatible with the null hypothesis, the next step is to decide whether to reject or not the null hypothesis according to the degree of compatibility with the null hypothesis.

01:55 And usually that's like an alpha value, 0 .05, we'll say.

02:00 If your p -value falls less than the alpha, you'd reject.

02:04 If not, you would fail to reject.

02:05 All right, so third question.

02:09 To test the hypothesis, the first step is to establish your null and alternative hypotheses.

02:13 The next step is to dot, dot, dot.

02:18 Well, once you've established these, notice a and b all use the word generate hypotheses.

02:27 So just simple, not simple, but just kind of looking at the question, you could ignore a and b because they talk about generating hypotheses, but right here, we've established the null...

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