An investigator thinks that people under the age of forty have vocabularies that are different than those of people over sixty years of age. The investigator administers a vocabulary test to a group of 31 younger subjects and to a group of 31 older subjects. Higher scores reflect better performance. The mean score for younger subjects was 14.0 and the standard deviation of younger subject's scores was 5.0. The mean score for older subjects was 20.0 and the standard deviation of older subject's scores was 6.0. Does this experiment provide evidence for the investigator's theory? Are these results meaningful? A. Please state both the null and alternative hypotheses. B. Select a significance level C. Please show all calculations needed to generate the appropriate statistic. D. State your decision as to whether the investigator should reject the null hypothesis. E. Calculate the effect size for each problem.
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The null hypothesis (H0) is that there is no difference in the vocabulary scores between people under forty and those over sixty. The alternative hypothesis (H1) is that there is a difference in the vocabulary scores between these two age groups. B. Let's select Show more…
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An investigator thinks that people under the age of forty have vocabularies that are different than those of people over sixty years of age. The investigator administers a vocabulary test to a group of 37younger subjects and to a group of 45older subjects. Higher scores reflect better performance. The mean score for younger subjects was 15and the standard deviation of younger subject's scores was 5. The mean score for older subjects was 20and the standard deviation of older subject's scores was 5.9. Does this experiment provide evidence for the investigator's theory?Useα=0.10) a. Write alternative. Do not write null hypothesis. Indicate the tail. b. Find test statistics (round to2decimals) c. Find P-value (round to 3decimal places). Can we reject the null hypothesis? d. Write the conclusion in the contest of the problem e. Find a 90% confidence interval for μ1–μ2 (round to2decimals)
Samriddhi S.
Sri K.
Please provide the following information. (a) What is the level of significance? State the null and alternate hypotheses. (b) Compute the sample test statistic. What is the sampling distribution? What conditions are necessary to use this distribution? (c) Find the $P$ -value of the sample test statistic. (d) Conclude the test. (c) Interpret the conclusion in the context of the application. Does the average length of time to earn a doctorate differ from one field to another? Independent random samples from large graduate schools gave the following averages for length of registered time (in years) from bachelor's degree to doctorate. Sample A was taken from the humanities field, and sample $B$ from the social sciences field (Reference: Education Statistics, U.S. Department of Education). \begin{array}{|c|cccccccccccc} \hline \text { Field A } & 8.9 & 8.3 & 7.2 & 6.4 & 8.0 & 7.5 & 7.1 & 6.0 & 9.2 & 8.7 & 7.5 & \\ \hline \text { Field B } & 7.6 & 7.9 & 6.2 & 5.8 & 7.8 & 8.3 & 8.5 & 7.0 & 6.3 & 5.4 & 5.9 & 7.7 \\ \hline \end{array} Use a $1 \%$ level of significance to test the claim that there is no difference in I the distributions of time to complete a doctorate for the two fields.
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