Question

multiple choice. choose the one alternative that best completes the statement or answers the question.
express the null hypothesis and the alternative hypothesis in symbolic form. use the correct symbol ($\mu$, $p$, $\sigma$) for the
indicated parameter.

1. carter motor company claims that its new sedan, the libra, will average better than 23 miles

per gallon in the city. use $\mu$, the true average mileage of the libra.
a) $h_0: \mu < 23$
b) $h_0: \mu = 23$
c) $h_0: \mu = 23$
d) $h_0: \mu > 23$
$h_1: \mu \geq 23$
$h_1: \mu < 23$
$h_1: \mu > 23$
$h_1: \mu \leq 23$

1. the owner of a football team claims that the average attendance at games is over 68,800, and he

is therefore justified in moving the team to a city with a larger stadium.
a) $h_0: \mu > 68,800$
b) $h_0: \mu = 68,800$
$h_1: \mu \leq 68,800$
$h_1: \mu > 68,800$
c) $h_0: \mu < 68,800$
d) $h_0: \mu = 68,800$
$h_1: \mu \geq 68,800$
$h_1: \mu < 68,800$

1. the manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed

3)
to maintain a true mean temperature, $\mu$, of $48^\circ f$, ideal for a certain type of german pilsner. the
owner of the brewery does not agree with the refrigerator manufacturer, and claims he can
prove that the true mean temperature is incorrect.
a) $h_0: \mu \geq 48^\circ$
b) $h_0: \mu \
eq 48^\circ$
c) $h_0: \mu = 48^\circ$
d) $h_0: \mu \leq 48^\circ$
$h_1: \mu < 48^\circ$
$h_1: \mu = 48^\circ$
$h_1: \mu \
eq 48^\circ$
$h_1: \mu > 48^\circ$

1. the principal of a middle school claims that test scores of the seventh - graders at her school vary

4)
less than the test scores of seventh - graders at a neighboring school, which have variation
described by $\sigma = 14.7$.
a) $h_0: \sigma > 14.7$
b) $h_0: \sigma < 14.7$
c) $h_0: \sigma = 14.7$
d) $h_0: \sigma = 14.7$
$h_1: \sigma \leq 14.7$
$h_1: \sigma > 14.7$
$h_1: \sigma < 14.7$
$h_1: \sigma > 14.7$
assume that the data has a normal distribution and the number of observations is greater than fifty. find the critical $z$
value used to test a null hypothesis.

1. $\alpha = 0.09$ for a right - tailed test.

a) $\pm 1.96$
b) $1.96$
c) $\pm 1.34$
d) $1.34$
5)

1. $\alpha = 0.1$ for a two - tailed test.

a) $\pm 2.052$
b) $\pm 1.645$
c) $\pm 2.33$
d) $\pm 1.4805$
6)

Explanation:

Step1: Hypothesis testing concepts

The null hypothesis \(H_0\) is a statement of no - effect or no - difference. The alternative hypothesis \(H_1\) is what we are trying to find evidence for.

• For the claim "average better than 23 miles per gallon", the null hypothesis is \(H_0:\mu = 23\) (assuming no improvement) and the alternative is \(H_1:\mu>23\).
• For the claim "average attendance is over 68800", \(H_0:\mu = 68800\) (no - change assumption) and \(H_1:\mu>68800\).
• For the claim about the temperature being incorrect (\(\mu

eq48^{\circ}\)), \(H_0:\mu = 48^{\circ}\) (manufacturer's claim) and \(H_1:\mu
eq48^{\circ}\).

• For the claim about variance being less than 14.7, \(H_0:\sigma = 14.7\) (neighboring school's variance) and \(H_1:\sigma<14.7\).
• For a right - tailed test with \(\alpha = 0.09\), we look up the \(z\) - value in the standard normal table. The \(z\) - value corresponding to an area of \(1 - 0.09=0.91\) in the left - tail is \(z = 1.34\).
• For a two - tailed test with \(\alpha=0.1\), the area in each tail is \(\frac{\alpha}{2}=0.05\). The \(z\) - values corresponding to areas of \(0.05\) in the tails are \(z=\pm1.645\).

Answer:

1. C. \(H_0:\mu = 23\), \(H_1:\mu>23\)
2. B. \(H_0:\mu = 68800\), \(H_1:\mu>68800\)
3. C. \(H_0:\mu = 48^{\circ}\), \(H_1:\mu

eq48^{\circ}\)

1. C. \(H_0:\sigma = 14.7\), \(H_1:\sigma<14.7\)
2. D. \(1.34\)
3. B. \(\pm1.645\)