t tests for a mean and the paired t-test Quiz

1. A sample of $16$ gives $\bar x=20$, $s=4$. For $H_0:\mu=19$, the test statistic is

• A. $1$
• B. $0.25$
• C. $4$
• D. $0.5$

2. A paired test has $12$ pairs. The degrees of freedom are

• A. $24$
• B. $12$
• C. $22$
• D. $11$

3. For a $99\%$ confidence interval from $n=10$, which value is used?

• A. the upper $1\%$ point of $t_9$
• B. the upper $0.5\%$ point of $t_9$
• C. the upper $0.5\%$ point of $t_{10}$
• D. $2.576$

4. Before and after readings are taken for the same $10$ patients. The correct approach is to

• A. use a two-sample test for independent samples
• B. find the differences and carry out a one-sample $t$-test on them
• C. use a $\chi^2$ test
• D. compare the two means with a $z$ test

5. A $95\%$ interval for $\mu$ is $(3.1,\ 4.9)$. A two-tailed $5\%$ $t$ test of $H_0:\mu=5.2$ would

• A. not reject $H_0$
• B. be impossible
• C. reject $H_0$ because $5.2$ lies outside the interval
• D. reject $H_0$ at the $1\%$ level