Exam 8: Inferences Based on a Single Sample: Tests of Hypothesis

n = 70, p0 = 0.9

If a hypothesis test were conducted using α = 0.05, to which of the following p-values would cause the null hypothesis to be rejected.

The alternative hypothesis is accepted as true unless there is overwhelming evidence that it is false.

It is desired to test H0: μ = 12 against Ha: μ ≠ 12 using α = 0.05. The population in question is uniformly distributed with a standard deviation of 2.0. A random sample of 100 will be drawn from this population. If μ is really equal to 11.9, what is the value of β associated with this test?

In a test of H0: μ = 250 against Ha: μ ≠ 250, a sample of n = 100 observations possessed mean $\bar { x }$ = 247.3 and standard deviation s = 11.4. Find and interpret the p-value for the test.

Consider a test of $\mathrm { H } _ { 0 } : \mu = 80$ performed with the computer. SPSS reports a two-tailed p-value of $0.0038$ . Make the appropriate conclusion for the given situation: $\mathrm { H } _ { \mathrm { a } } : \mu \neq 80 , z = 2.9 , \alpha = 0.04$ A) Reject $\mathrm { H } _ { 0 }$ B) Fail to reject $\mathrm { H } _ { 0 }$

In a test of hypothesis, the sampling distribution of the test statistic is calculated under the assumption that the alternative hypothesis is true.

A random sample of 8 observations from an approximately normal distribution is shown below. 5 6 4 5 8 6 5 3 Find the observed level of significance for the test of H0: μ = 5 against Ha: μ ≠ 5. Interpret the result.

The rejection region for a two-tailed test with α = .05 is -1.96 < z < 1.96.

The null hypothesis represents the status quo to the party performing the sampling experiment.

Suppose we wish to test $H _ { 0 } : \mu = 23$ vs. $H _ { \mathrm { a } } : \mu < 23$ . Which of the following possible sample restults gives the most evidence to support $H _ { a }$ (i.e., reject $H _ { 0 }$ )? A) $\bar { x } = 19 , s = 5$ B) $\bar { x } = 20 , s = 8$ C) $\bar { x } = 21 , s = 6$ D) $\bar { x } = 19 , s = 11$

In a test of H0: μ = 12 against Ha: μ > 12, a sample of n = 75 observations possessed mean $\bar { x }$ = 13.1 and standard deviation s = 4.3. Find and interpret the p-value for the test.

$\alpha = 0.08 , \mathrm { p } \text {-value } = 0.001$ A) Reject $\mathrm { H } _ { 0 }$ B) Fail to reject $\mathrm { H } _ { 0 }$

A random sample of n observations, selected from a normal population, is used to test the null hypothesis H0: σ2 = 155. Specify the appropriate rejection region. Ha: σ2 > 155, n = 25, α = .10

The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion exceeds 25%, then the lab will scale back a proposed enlargement of its facilities. Suppose 250 business students were randomly sampled and 65 have laptops. What assumptions are necessary for this test to be satisfied?

A company reports that 80% of its employees participate in the company's stock purchase plan. A random sample of 50 employees was asked the question, "Do you participate in the stock purchase plan?" The answers are shown below. yes no no yes no no yes yes no no no yes yes yes no yes no no yes yes no yes yes no yes yes no yes yes yes yes no no yes yes yes yes yes no yes no yes yes no yes yes yes yes yes yes Perform the appropriate test of hypothesis to investigate your suspicion that fewer than 80% of the company's employees participate in the plan. Use α = .05.

An industrial supplier has shipped a truckload of teflon lubricant cartridges to an aerospace customer. The customer has been assured that the mean weight of these cartridges is in excess of the 10 ounces printed on each cartridge. To check this claim, a sample of n = 10 cartridges are randomly selected from the shipment and carefully weighed. Summary statistics for the sample are: $\bar { x }$ = 10.11 ounces, s = .30 ounce. To determine whether the supplier's claim is true, consider the test, H0: ? = 10 vs. Ha: ? > 10, where ? is the true mean weight of the cartridges. Find the rejection region for the test using ? = .01.

The hypotheses for $H _ { 0 } : \mu = 65 \text { and } H _ { \mathbf { a } } : \mu > 65 \text { are tested at } \alpha = .05$ . Sketch the appropriate rejection region.

A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 238 students and asked each to provide the amount of time they spent traveling to campus. This variable, travel time, was then used to create a confidence interval and to conduct a test of hypothesis, both of which are shown in the printout below. One-Sample Z Test Null Hypothesis: $\mu = 20$ Alternative Hyp: $\mu > 20$ $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$95 \% \text { Conf Interval }$ $\text { Variable \quad Mean \quad SE \quad Lower \quad Upper\quad Z \quad P }$ Camera Price 23.243 1.3133 20.669 25.817 2.47 0.0071 Cases Included 238 What conclusion can be made from the test of hypothesis conducted in this printout? Begin each answer with, "When testing at ? = 0.01…"