Question

A business journal investigation of the performance and timing of corporate acquisitions discovered that in a random sample of 2 comma 628 ?firms, 693 announced one or more acquisitions during the year 2000. Does the sample provide sufficient evidence to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 29 ?%? Use alpha equals0.01 to make your decision. What are the hypotheses for this? test? A. H0?: pgreater than 0.29Ha?: pless than or equals 0.29 B. H0?: pequals 0.29Ha?: pgreater than 0.29 C. Upper H 0 : p equals 0.29 Upper H Subscript a Baseline : p less than 0.29 D. H0?: pnot equals 0.29Ha?: pequals 0.29 E. H0?: pless than 0.29Ha?: pequals 0.29 F. H0?: pequals 0.29Ha?: pnot equals 0.29 What is the rejection? region? Select the correct choice below and fill in the answer? box(es) to complete your choice. ?(Round to two decimal places as? needed.) A. zgreater than nothing B. zless than nothing or zgreater than nothing C. zless than nothing Calculate the value of the? z-statistic for this test. zequals nothing ?(Round to two decimal places as? needed.) What is the conclusion of the? test? ? the null hypothesis because the test statistic ? is not is in the rejection region.? Therefore, there is ? insufficient sufficient evidence at the 0.01 level of significance to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 29 ?%.

Answer 1

A. Here claim is that p is less than 0.29

$H_0:p=0.29$ vs $H_1:p<0.29$

b. The z-critical value for a left-tailed test, for a significance level of ?=0.01 is

zc?=?2.33

Graphically

Critical Values Normal Distribution 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 4.0 -3.5-3.0 -2.5 -2.0 15 1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

c. Here $\widehat{p}=\frac{693}{2628}=0.26$

$SEp=\sqrt{\frac{pq}{n}}=\sqrt{\frac{0.29*0.71}{2628}}=0.0089$

Hence test statistics is $z=\frac{\widehat{p}-p}{SEp}=\frac{0.26-0.29}{0.0089}=-3.37$

d. As z statistics falls in the rejection region, we reject the null hypothesis

Hence there is sufficient evidence at the 0.01 level of significance to indicate that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 29 ?%.