Question

A business journal investigation of the performance and timing of corporate acquisitions discovered that in a random sample of 2 comma 6402,640 ​firms, 709709 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 2929​%? Use alphaαequals=0.100.10 to make your decision.

Answer 1

Explanation:

Using the one sample proportion test:

z = (p-P) / √{P (1-P)/n}

Where p = 709/2640= 0.27, P = 0.29, n= 2640

Thus z = (0.27-0.29) / √{0.29 (1-0.29) / 2640}

z = (-0.02) / √{0.29(0.71) /2640}

z = (-0.02) / √0.00007799

z = (0.02) / 0.0088

z = 2.27

To be able to draw a conclusion, lets find the p value at the 0.1 level of significant: p value is 0.2327. The result is significant as the p value is greater than 0.1 thus we will fail to reject the null and conclude that there is not enough statistical evidence to prove that the true percentage of all firms that announced one or more acquisitions during the year 2000 is less than 29%