Question

According to a nation wide survey, only 30% of adult Americans had a will. A researcher in Utah suspects that the proportion of adults in Utah with wills is less than the national proportion. Suppose this researcher takes a survey of 1000 adult Utah residents and finds that 277 report having wills. (round your answers to four decimal places)

part b: Calculate and report the value of the test statistic.

part c: Calculate and report the p-value and then use the p-value approach to determine at a 10% level of significance if the proportion of adult Utah residents that have a will is less than the national proportion.

part d: Determine and report the critical value(s) for a 10% level of significance and use the critical value approach to determine if the proportion of adult Utah residents that have a will is less than the national proportion.

Answer 1

Solution :- Let x be the number of American adult had a will in Utah X = 271, n = 1000 Sample proportion ê is. 277 TE 1000 = 0.277 å= 1 P = 1-0.277 = 0.7 23 lovel ant ad The hypothesig is to be tested Ho: p=0.30 uitrogor DO 100 vs He: p < 0.30 : puro 0 * Part but Test statistic under Ho is. 2 = Pr Pt ? n 0.30-0.277 0.277X0.7 23 1000 13 119 % 0.023 le lor 0.0141 origo TOIT todo

7 = 1.6812 part co p-value of the test is. P-value = P[z<p cal] =P[< < 1-6312] = 1 -0.0514 p-value = 0.9486 Let Q = 0.10 be the level of significance. Here p-value = 0.9486 > 0.10 we accept Ho at 10olo level of significance. * By p-value approgeh, it is conclude that proportion of Utah may be equal to national proportion , con otot part de The critical value of the test is. 70.10. Za. - 1-28 :( from normal statistical table) Here 7 = 1.63 12 7 – La -1.28 , We accept Ho. at 10 olo level of significance. * Conclusion :- By Critical value approach, it is concluded that proportion of Utah may be equal to national proportion.