Question

A Telecommunications company recently installed a new speech recognition system for its repair calls. In their old system, operators had to press keys on the numeric keypad to answer questions, which led many callers to opt to talk to an operator instead. Under the old system, 94% of the customers had to talk to an operator to get their needs met. They want to do a hypothesis test to determine if the new system has been successful in reducing the proportion of customers that need to talk to human operators. Suppose that using the new system a sample of 150 customer calls showed that 135 customers required an operator, using a 5% significance level the correct conclusion is Reject Ho, There is insufficient evidence that the new system has reduced the proportion of customers that need to talk to human operators to get their needs met Reject Ho, There is sufficient evidence that the new system has reduced the proportion of customers that need to talk to human operators to get their needs met ODo Not Reject Ho, There is sufficient evidence that the new system has reduced the proportion of customers that need to talk to human operators to get their needs met O Do Not Reject Ho, There is insufficient evidence that the new system has reduced the proportion of customers that need to talk to human operators to get their needs met

Answer 1

H0: p = 0.94

Ha: p < 0.94

Sample proportion $\hat{p}$ = 15 / 150 = 0.90

Test statistics

z = $\hat{p}$ - p / sqrt( p( 1 - p) / n)

= 0.90 - 0.94 / sqrt( 0.94 * 0.06 / 150)

= -2.06

This is test statistics value.

Critical value at 0.05 level is -1.645

Since test statistics < -1.645, we have sufficient evidence to reject H0.

We conclude at 0.05 level that,

Reject H0. There is sufficient evidence that the new system has reduced the proportion of customers

that need to talk to human operators to get their needs met.