Question

Perform a one-tailed test. Set up H0 and Ha. Compute test statistic and p-value. Draw conclusions. For both questions.

#1. A Gallup survey conducted April 2–11, 2018, found that 152 out of 1015 American adults mentioned immigration/illegal aliens as the most important problem facing the nation. An earlier survey conducted in February 2011 found that 108 out of 978 American adults mentioned immigration/illegal aliens as the most important problem facing the nation. Can we conclude that the percentage of all American adults who believed that immigration/illegal aliens was the most important problem facing the nation was increased in 2018 compared to that in 2011?

#2. The District of Columbia Opportunity Scholarship Program was created by Congress to provide tuition vouchers to low-income parents who want their child to attend a private school.

In 2012–2014, a treatment group of 995 students were randomly selected to receive a tuition

voucher, while a control group of 776 students did not receive vouchers. One year later, the

students were given a standardized reading test. The average score of the students in the treatment group was 601.78 with a standard deviation of 52.65; the average score of the control group was 605.78 with a standard deviation of 55.73. At the α=0.01 level of significance, can we conclude that the average reading score of students who receive a tuition voucher to attend private school is lower than the average reading score of students who do not receive a tuition voucher?

Answer 1

= 152 1015 = 0.1498 aliens was the most problem the nation Ô Cproportion of American Adult who belived that immigration the most important facing in 2018) Pa Gpaparution of American Adelh who belined that immigration aliens was the mat important 2 108 978 - 0.1104 problem facing the nation in 2011 Level Well hy pothesis Ho : p. <P2 Alternative hypothesis He: po > pa of significance (2) = 0.05 (stand and valuu) Ri - Vp (1-P) G ++) Test statistic J> 152 + 108 260 - 0.1305 - 1015 + 978 1993 0.1498 0.1104 Test statistic 6.1305 x 0.8695 x (1o15 +976) :-. Test statistic 2.610 f! p-value = 0.0045 [source source - STATKEY Cimape at attached

level of significance and concluch that average 9 conclusion - As the p-value (0.0045) < x 10.05) , we Reject the Null hypothesis at 51 level of significance and and conclude that perantage of all American adult who belived that immigrations illegal alien was the most important problem facing nation increased in 2018 compared that in 2011. to the was group (did not recieve vorecher) 2 Treatment group creceived rouches) 601.78 Control X = 605.78 S2 = 55.73 m₂ = 776. Xi S, = 52-65 n = 995 Ha Mi <M2 : Null hy nothosis : Ho: Mizuz Alternative hypothesis of significance L = 0-01 Level Xi NTI 601.78 – 605.78 Za = Test statistic 52² 9,2 vmi 52-652 995 + 55.73? 776 Test statistic Z - 1.535 0.062 = P-value 9 [ Source - STAT KEY Cimage attached] Conclusion – As the pralie (0.062) > (0.01), Fail to Reject the Null hy rothsis at 1% reading some of students who sreceived tution voucher average reading score students who do not receive a g tuition voucher 7 eosd.odt CILA doo

Statkey Theoretical Distribution Normal Distribution- Reset Plot Normal Distribution Left Tail Two-Tail Right Tail Mean Standard Deviation 0.40 0 1 0.35 Edit Parameters 0.30 0.25 0.20 0.0045 0.15 0.10 0.05 0.00 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 2.610 Activate Windows

Statkey Theoretical Distribution Normal Distribution Reset Plot Normal Distribution Left Tail Two-Tail Right Tail Mean Standard Deviation 0.40 0 0.35 Edit Parameters 0.30 0.25 0.20 0.062 0.15 0.10 0.05 0.00 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 -1.535 Activate Windows

The test statistic is calculated using the formula mentioned. The p value is obtained from STATKEY (image attached for reference). We compare the p value with alpha and make the required decision.