One-sample t-test Quiz

1. A random sample of $15$ values is taken from a normal population with unknown variance. How many degrees of freedom are used in a test of the mean?

• A. $15$
• B. $13$
• C. $14$
• D. $16$

2. A sample of $16$ has $\bar x=52$ and $s=4$. Calculate $t$ for $H_0:\mu=50$.

• A. $0.5$
• B. $2.0$
• C. $8.0$
• D. $0.125$

3. In a one-tailed test of $H_1:\mu>\mu_0$ with $\nu=9$ at $5\%$, the critical value is $1.833$ and $t=1.9$. What is the conclusion?

• A. Reject $H_0$: evidence that the mean is greater than $\mu_0$
• B. Do not reject $H_0$ because $1.9$ is small
• C. Reject $H_0$: evidence that the mean is less than $\mu_0$
• D. The test is invalid because $n$ is small

4. Why is a $t$-distribution used instead of the normal distribution?

• A. The population variance is known
• B. The sample is large
• C. The population is not normal
• D. The population variance is unknown and estimated from a small sample

5. Which assumption is needed for a one-sample $t$-test?

• A. The sample is larger than $30$
• B. The population variance is known
• C. The population is normally distributed
• D. The sample mean equals $\mu_0$