1215

Which of the following statements about hypothesis testing is least accurate?

A) A Type I error is the probability of rejecting the null hypothesis when the null hypothesis is false.

B) The significance level is the probability of making a Type I error.

C) A Type II error is the probability of failing to reject a null hypothesis that is not true.

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A Type I error is the probability of rejecting the null hypothesis when the null hypothesis is true.

1215

A pitching machine is calibrated to deliver a fastball at a speed of 98 miles per hour. Every day, a technician samples the speed of twenty-five fastballs in order to determine if the machine needs adjustment. Today, the sample showed a mean speed of 99 miles per hour with a standard deviation of 1.75 miles per hour. Assume the population is normally distributed. At a 95% confidence level, what is the t-value in relation to the critical value?

A) The critical value exceeds the t-value by 1.3 standard deviations.

B) The t-value exceeds the critical value by 0.8 standard deviations.

C) The t-value exceeds the critical value by 1.5 standard deviations.

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t = (99 – 98) / (1.75 / √25) = 2.86. The critical value for a two-tailed test at the 95% confidence level with 24 degrees of freedom is ±2.06 standard deviations. Therefore, the t-value exceeds the critical value by 0.8 standard deviations.