Attitudes In the study of older students’ attitudes from...

Attitudes In the study of older students’ attitudes from Exercise 3, the sample mean SSHA score was 125.7 and the sample standard deviation was 29.8. A significance test yields a P-value of 0.0101. (a) Interpret the P-value in context. (b) What conclusion would you make if $\alpha=0.05$ ? If $\alpha=0.01$ Justify your answer.

Attitudes In the study of older students’ attitudes from Exercise 3, the sample mean SSHA score was
125.7 and the sample standard deviation was 29.8. A significance test yields a P-value of 0.0101.
(a) Interpret the P-value in context.
(b) What conclusion would you make if $\alpha=0.05$ ? If $\alpha=0.01$ Justify your answer.

Key Concepts

P-value

The P-value is a probability that measures the strength of the evidence against the null hypothesis. It indicates the likelihood of observing a test statistic at least as extreme as the one obtained from the sample data, assuming that the null hypothesis is true. A low P-value suggests that such an extreme observed result would be unlikely under the null hypothesis, thereby providing evidence in favor of the alternative hypothesis.

Significance Level

The significance level, denoted by alpha (?), is the threshold the researcher sets to decide whether the observed effect is statistically significant. It represents the maximum allowable probability of incorrectly rejecting the null hypothesis (committing a Type I error). Common significance levels are 0.05 and 0.01, with lower values leading to more conservative decisions regarding rejecting the null hypothesis.

Hypothesis Testing Decision Rule

In hypothesis testing, if the P-value is less than the chosen significance level (?), the null hypothesis is rejected in favor of the alternative hypothesis. Conversely, if the P-value is greater than or equal to ?, there is insufficient evidence to reject the null hypothesis. For instance, with an ? of 0.05 a P-value of 0.0101 would lead to rejecting the null hypothesis, while with an ? of 0.01 the decision might differ if the P-value does not meet the stricter threshold.

Transcript

00:01 The mean score for the u .s.

00:03 College student is about 115 on the survey of study habits and attitudes.

00:09 Now, a teacher suspects that older students have better attitudes towards school, so she gives the ssha to an srs of 45 of the over 1 ,000 students at her college who are at least 30 years of age.

00:25 Now, the results come in as an average of 125 .7 with an average standard deviation of 29 .8, and a significant test gives a p value of 0 .01.

00:42 Now, in context, what this p value really means is that if the population average was 115, then there is a 1 .01 % chance of getting the average of a 125 .7 in this survey.

01:17 So again, if the population mean is equal, if the null hypothesis is true, that the population mean is 115, then we would have a 1.

01:31 1 .01 % chance of obtaining a random sample with a sample mean of 125 .7 or more.

01:51 So that's kind of what this p value means.

01:54 Now that 1 % is very small.

01:57 So let's judge this against an alpha of 0 .05.

02:03 And so if we had an alpha of 0 .05 and our p value is 0 .0101, we would say that because the p value is less than the 0 .05, we reject our null hypothesis of this put hypo.

02:33 Now, in this context, we would say we would say we have convincing evidence that the true mean score on the ssha for all students at least 30 years of age at the teachers college is greater than 115.

03:09 So again, we take our p -value and we check it with the alpha.

03:14 And because our p value is less than 0 .05, we say that we reject the null hypothesis...

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