Question

A random sample of 500 hand written telephone number digits is analyzed. It is determined that your company’s optical character recognition software correctly identified 457 of them. Samsung would like to know whether the rate is greater than 90% correct before they consider buying your software for use in the Galaxy S 23. Do the data provide evidence that the rate is greater than 90% at ??=??.?????

Answer 1

H0: p <= 0.90

Ha: p > 0.90 (Right tailed)

Sample proportion = 457 / 500 = 0.914

Test statistics

Z = - p / sqrt( p (1 - p) / n)

= 0.914 - 0.90 / sqrt( 0.9 * 0.1 / 500)

= 1.04

This is test statistics value.

Critical value at 0.05 level is 1.645.

Since test statistics value < 1.645, we do not have sufficient evidence to reject H0.

p-value = P( Z > z) = P(Z > 1.04) = 0.1492

We conclude at 0.05 level that we fail to support the claim that rate is greater than 90%.