## Elementary Statistics (12th Edition)

Published by Pearson

# Chapter 8 - Hypothesis Testing - 8-4 Testing a Claim About a Mean - Basic Skills and Concepts - Page 421: 19

#### Answer

There is sufficient evidence to support that the mean time to achieve a bachelor's degree is more than 4 years.

#### Work Step by Step

$H_{0}:\mu=4$. $H_{a}:\mu >4.$ Hence the value of the test statistic: $\frac{\overline{x}-\mu}{s/\sqrt n}=\frac{6.5-4}{3.5056/\sqrt{20}}=3.189.$ The P-value is the interval of probabilities between which the value of the test-statistic lies in the table with degree of freedom=sample size-1=20-1=19, hence P is less than 0.005. If the P-value is less than $\alpha$, which is the significance level, then this means the rejection of the null hypothesis. Hence:P is less than $\alpha=0.01$, because it is less than 0.005, hence we reject the null hypothesis. Hence we can say that there is sufficient evidence to support that the mean time to achieve a bachelor's degree is more than 4 years.

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