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Thanks to an initiative to recruit top students, an administrator at a college claims that this year's entering class must have a greater mean IQ score than tha of entering classes from previous years. The administrator tests a random sample of 11 of this year's entering students and finds that their mean IQ score is 112, with a standard deviation of 15. The college records indicate that the mean IQ score for entering students from previous years is 110. Is there enough evidence to conclude, at the 0.05 level of significance, that the population mean IQ score, μ, of this year's class is greater than that of previous years? To answer, assume that the IQ scores of this year's entering class are approximately normally distributed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)

Thanks to an initiative to recruit top students, an administrator at a college claims that this year's entering class must have a greater mean IQ score than tha of entering classes from previous years. The administrator tests a random sample of 11 of this year's entering students and finds that their mean IQ score is 112, with a standard deviation of 15. The college records indicate that the mean IQ score for entering students from previous years is 110. Is there enough evidence to conclude, at the 0.05 level of significance, that the population mean IQ score, μ, of this year's class is greater than that of previous years? To answer, assume that the IQ scores of this year's entering class are approximately normally distributed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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Thanks to an initiative to recruit top students, an administrator at a college claims that this year's entering class must have a greater mean IQ score than that of entering classes from previous years. The administrator tests a random sample of 11 of this year's entering students and finds that their mean IQ score is 112, with a standard deviation of 15. The college records indicate that the mean IQ score for entering students from previous years is 110. Is there enough evidence to conclude, at the 0.05 level of significance, that the population mean IQ score, μ, of this year's class is greater than that of previous years? To answer, assume that the IQ scores of this year's entering class are approximately normally distributed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H₁. H : H₁ :0 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) n (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we conclude that the mean IQ score of this year's class is greater than that of previous years? Yes No 3 XI ロ=ロ 0#0 X a S OSO O<O р <Q 010 □<口
Transcribed Image Text:Thanks to an initiative to recruit top students, an administrator at a college claims that this year's entering class must have a greater mean IQ score than that of entering classes from previous years. The administrator tests a random sample of 11 of this year's entering students and finds that their mean IQ score is 112, with a standard deviation of 15. The college records indicate that the mean IQ score for entering students from previous years is 110. Is there enough evidence to conclude, at the 0.05 level of significance, that the population mean IQ score, μ, of this year's class is greater than that of previous years? To answer, assume that the IQ scores of this year's entering class are approximately normally distributed. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H₁. H : H₁ :0 (b) Determine the type of test statistic to use. (Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) n (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we conclude that the mean IQ score of this year's class is greater than that of previous years? Yes No 3 XI ロ=ロ 0#0 X a S OSO O<O р <Q 010 □<口
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