51% of students entering four-year colleges receive a degree within six years. Is this percent smaller than for students who play intramural sports? 140 of the 297 students who played intramural sports received a degree within six years. What can be concluded at the level of significance of αα = 0.01?The null and alternative hypotheses would be: Ho: ? p μ Select an answer < > ≠ = (please enter a decimal) H1: ? μ p Select an answer > = < ≠ (Please enter a decimal)The test statistic ? t z = (please show your answer to 3 decimal places.)The p-value = (Please show your answer to 4 decimal places.)

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Description: 51% of students entering four-year colleges receive a degree within six years. Is this percent smaller than for students who play intramural sports? 140 of the 297 students who played intramural sports received a degree within six years. What can be

1. Denote p as the true population proportion of students entering four-year colleges receive a degree within six years.It is needed to check, whether 51% of students, who entering four-year colleges receive a degree within six years, is smaller than for students who play intramural sports. The null and alternative hypotheses are: Null hypothesis: H0: p = 0.51. Alternative hypothesis: H1: p < 0.51. The direction of the test is left tailed. Hence, it is a left-tailed test.1. The level of significance is α = 0.01. If x denotes the number of cases favourable to an event in a sample of size n, then the sample proportion is, p̂ = x/n. According to the given question, in a sample of 1297 students 140 played intramural sports received a degree within six years. Thus, x = 140 and n = 297. Thus, p̂ = 0.471380 (= 140/297). The test statistic is: z0 = (p̂ – p0)/ √[p0 (1 – p0)/n] [Where p0 is the proportion value suggested in H0] = (0.471380 – 0.51) / √ [(0.51) (1 – 0.51)/297] = –0.03862/0.029007139 ≈ –1.331. Thus, the test statistic value is –1.331.2. Using the Excel formula =NORM.S.DIST(-1.331,TRUE), the p-value is 0.0916. Decision rule: If p-value is less than or equal to the level of significance, then reject the null hypothesis. Otherwise, failed to reject the null hypothesis. Here, the p-value is 0.0916, which is greater than the level of significance of 0.01. Hence, fail to reject the null hypothesis. There is not enough evidence to claim that the given percentage is smaller than for students who play intramural sports, at 1% level of significance.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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51% of students entering four-year colleges receive a degree within six years. Is this percent smaller than for students who play intramural sports? 140 of the 297 students who played intramural sports received a degree within six years. What can be concluded at the level of significance of αα = 0.01?

The null and alternative hypotheses would be:
Ho: ? p μ Select an answer < > ≠ = (please enter a decimal)
H₁: ? μ p Select an answer > = < ≠ (Please enter a decimal)

The test statistic ? t z = (please show your answer to 3 decimal places.)
The p-value = (Please show your answer to 4 decimal places.)

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