Question

A consulting group recently conducted a global survey of product teams with the goal of better understanding the dynamics of product team performance and uncovering the practices that make these teams successful. One of the survey findings was that 36​% of organizations have a coherent business strategy that they stick to and effectively communicate. Suppose another study is conducted to check the validity of this​ result, with the goal of proving that the percentage is less than 36​%. Complete parts​ (a) and​ (b) below.

a. State the null and research hypotheses. Identify the null and alternative hypotheses.

b. A sample of 100organizations is​ selected, and results indicate that 30 organizations have a coherent business strategy that they stick to and effectively communicate. Use the​ p-value approach to determine at the 0.05 level of significance whether there is evidence that the percentage is less than 36​%. Calculate the test statistic.

Identify the value of the​ p-value from your technology output. Recall that this is a​ lower-tail test.

Reject or not reject?

Answer 1

a) The null and alternative hypotheses are,

H0 : p = 0.36

Ha : p < 0.36

b) sample size (n) = 100 and x = 30

=> sample proportion $(\hat p)$ = 30/100 = 0.30

Test statistic is,

2-p-p Polt=p) 0.30 – 0.361 0.360(1-0.36) = -1.2 == 0.36*(1-0.36) -1.25 p*(1- 100

Test statistic = -1.25

p-value = P(Z < -1.25) = 0.1056

=> p-value = 0.1056

Since, p-value = 0.1056 > 0.05, we do not reject H0.