A Department of Mathematics at a University claims in an advertisement that the mean math SAT scores of its majors is at least 600. Admissions at the University wants to make sure that the statement of the Department of Mathematics is a reasonable one and decides to test the claim using a significance level of 0.10 with a random sample of 16 math majors. The results are below. SAT scores are normally distributed with a population standard deviation of 15. 600 600 580 570 610 620 560 630 650 610 570 610 550 560 580 620 State your conclusion in words. There is not sufficient evidence to warrant rejection of the claim that the mean math SAT scores of its majors is at least 600. There is sufficient evidence to warrant rejection of the claim that the mean math SAT scores of its majors is at least 600. The sample data support the claim that the mean math SAT scores of its majors is at least 600. There is not sufficient sample evidence to support the claim that the mean math SAT scores of its majors is at least 600.
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SAT Reasoning Test In $2005,$ in response to various criticisms, the College Board implemented changes to the SAT test. In particular, the math portion eliminated quantitative comparisons and expanded the topics covered. A school administrator believes that the new math portion is more difficult and will result in lower scores on the math portion compared to the 2004 average score of 516. A random sample of 25 students taking the new SAT test resulted in the following scores on the math portion. $$\begin{array}{lllllllll} 410 & 720 & 480 & 560 & 590 & 340 & 430 & 400 & 440 \\ \hline 540 & 480 & 450 & 720 & 570 & 380 & 740 & 640 & 600 \\ \hline 320 & 580 & 450 & 480 & 550 & 470 & 380 & & \end{array}$$ (a) Because the sample size is small, he must verify that the new math scores are normally distributed and the sample does not contain any outliers. The normal probability plot and boxplot are shown. Are the conditions for testing the hypothesis satisfied? (b) Do you believe students scored lower? Assume $$\sigma=114$$ FIGURE CANT COPY
Hypothesis Tests Regarding a Parameter
Hypothesis Tests for a Population Mean Assuming the Population Standard Deviation Is Known
The mean SAT score in mathematics, μ , is 561 . The standard deviation of these scores is 32 . A special preparation course claims that its graduates will score higher, on average, than the mean score 561 . A random sample of 70 students completed the course, and their mean SAT score in mathematics was 563 . At the 0.1 level of significance, can we conclude that the preparation course does what it claims? Assume that the standard deviation of the scores of course graduates is also 32 . Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. The null hypothesis: H 0 : The alternative hypothesis: H 1 : The type of test statistic: The value of the test statistic: (Round to at least three decimal places.) The p-value: (Round to at least three decimal places.) Can we support the preparation course's claim that its graduates score higher in SAT?
Ana Carolina D.
The Scholastic Aptitude Test (SAT) contains three areas: critical reading, mathematics, and writing. Each area is scored on an 800-point scale. A sample of SAT scores for six students follows. Student Critical Reading Mathematics Writing 1 528 534 528 2 592 590 588 3 465 464 445 4 561 566 553 5 436 478 430 6 430 458 420 Using a 0.05 level of significance, do students perform differently on the three areas of the SAT? State the null and alternative hypotheses. H0: 𝜇Reading = 𝜇Mathematics = 𝜇Writing Ha: 𝜇Reading ≠ 𝜇Mathematics ≠ 𝜇Writing H0: 𝜇Reading ≠ 𝜇Mathematics ≠ 𝜇Writing Ha: 𝜇Reading = 𝜇Mathematics = 𝜇Writing H0: 𝜇Reading = 𝜇Mathematics = 𝜇Writing Ha: Not all the population means are equal. H0: At least two of the population means are equal. Ha: At least two of the population means are different. H0: Not all the population means are equal. Ha: 𝜇Reading = 𝜇Mathematics = 𝜇Writing Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. Reject H0. There is not sufficient evidence to conclude that the mean scores for the three parts of the SAT are not all equal. Reject H0. There is sufficient evidence to conclude that the mean scores for the three parts of the SAT are not all equal. Do not reject H0. There is not sufficient evidence to conclude that the mean scores for the three parts of the SAT are not all equal. Do not reject H0. There is sufficient evidence to conclude that the mean scores for the three parts of the SAT are not all equal. Which area of the test seems to give the students the most trouble? Explain. The mean test scores for the three sections are ? for critical reading, ? for mathematics, and ? for writing. Because the ? section has the lowest average score, this section appears to give the students the most trouble.
Chai S.
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