Hypothesis Testing Quiz with Answers (t, z, χ²)

Question 1

A company claims its light bulbs last **more than** 1000 hours on average. Let $\mu$ be the true mean lifetime. Which pair of hypotheses matches this claim?

Accepted Answer

$H_0: \mu = 1000,\quad H_a: \mu > 1000$

Answer

$H_0: \mu 
e 1000,\quad H_a: \mu = 1000$

Answer

$H_0: \mu > 1000,\quad H_a: \mu \le 1000$

Answer

$H_0: \mu \ge 1000,\quad H_a: \mu < 1000$

Question 2

A 90% confidence interval for a mean is $(12.4,\ 15.6)$. Which statement is correct?

Accepted Answer

If we repeated the sampling many times, about 90% of the constructed intervals would contain $\mu$

Answer

90% of the data values lie between 12.4 and 15.6

Answer

There is a 90% probability that $\mu$ lies between 12.4 and 15.6 for this dataset

Answer

The margin of error is $15.6-12.4=3.2$

Question 3

A sample of $n=25$ has $\bar{x}=82$ and $s=10$. Test $H_0: \mu=78$ vs. $H_a: \mu>78$ at $\alpha=0.05$. The test statistic is $t=2.0$ with $df=24$. Using $t_{0.95,24}\approx 1.711$, what is the correct conclusion?

Accepted Answer

Reject $H_0$ because $2.0>1.711$

Answer

Fail to reject $H_0$ because you must use a z-test when $n\ge 25$

Answer

Reject $H_0$ only if $p<0.025$ since $\alpha=0.05$ is split in half

Answer

Fail to reject $H_0$ because $2.0<1.711$

Hypothesis Testing Quiz with Answers (t, z, χ²)

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