22.20 Using the Internet. In 2013, 81.8% of first-year college students respondi

Question

22.20 Using the Internet. In 2013, 81.8% of first-year college students responding to a national survey said that they used the Internet frequently for research or homework. Administrators at a large state university believe that their current first- year students use the Internet more frequently than students in 2013 did. They find that 168 of an SRS of 200 of the university's first-year students said that they used 976 the Internet frequently for research or homework. Is the proportion of first-year students at this university who said that they used the Internet frequently for research or homework larger than the 2013 national value of 81.8%? (a) Explain in words what the parameter P is in this setting. (b) What are the null and alternative hypotheses Ho and Ha? (c) What is the numerical value of the sample proportion p^? The P-value is the probability of what event? (d) The P-value is P = 0.210. Explain carefully why this evidence should lead administrators to fail to reject Ho.

Explanation / Answer

(a) Here paraemeter P in this setting is proportion of first year students at the university who said that they used the internet facility for research and homework in the current year

(b) H0 : p = 0.818

H0 : p > 0.818

(c) Sample proportion p^ = 168/200 = 0.84

standard error of proportion = sqrt [0.818 * (1 - 0.818)/200] = 0.0273

Z = (0.84 - 0.818)/ 0.0273 = 0.8064

Here p - value = Pr(Z > 0.8064) = 1 - Pr(Z < 0.8064) = 1 - 0.7900 = 0.2100

Here the p - value we calculated 0.21 is the probability of proportion of first year students at the university who said that they used the internet facility for research and homework in the current year is greater or equal to 0.84, when the truw proportion is same as in 2013.

(d) Here P- value < 0.05, so there is not enough evidence which would lead administrators to reject null hypothesis. So, we will fail to reject null hypothesis here.

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