stats analysis test 2

It is known that the population variance equals 484. With a 0.95 probability, the sample size that needs to be taken to estimate the population mean if the desired margin of error is 5 or less is

75

If a hypothesis is not rejected at a 5% level of significance, it will

also not be rejected at the 1% level

For a two-tailed hypothesis test about μ, we can use any of the following approaches except

compare the level of significance to the confidence coefficient

The sample size that guarantees all estimates of proportions will meet the margin of error requirements is computed using a planning value of p equal to

.50

n = 49 H0: μ = 50 X = 54.8 Ha: μ ≠ 50 σ = 28 Refer to Exhibit 9-3. The test statistic equals

1.2

To estimate a population mean, the sample size needed to provide a margin of error of 2 or less with a .95 probability when the population standard deviation equals 11 is

117

In an analysis of variance problem if SST = 120 and SSTR = 80, then SSE is

40

A random sample of 25 statistics examinations was taken. The average score in the sample was 76 with a variance of 144. Assuming the scores are normally distributed, the 99% confidence interval for the population average examination score is

69.82 to 82.18

A sample of 26 elements from a normally distributed population is selected. The sample mean is 10 with a standard deviation of 4. The 95% confidence interval for μ is

8.462 to 11.538

Exhibit 8-1 In order to estimate the average time spent on the computer terminals per student at a local university, data were collected from a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.2 hours. Refer to Exhibit 8-1. If the sample mean is 9 hours, then the 95% confidence interval is approximately

8.74 to 9.26 hours

In the past, 75% of the tourists who visited Chattanooga went to see Rock City. The management of Rock City recently undertook an extensive promotional campaign. They are interested in determining whether the promotional campaign actually increased the proportion of tourists visiting Rock City. The correct set of hypotheses is

H0: p ≤ 0.75 Ha: p > 0.75

A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. Any overfilling or underfilling results in the shutdown and readjustment of the machine. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is

H0: μ = 12 Ha: μ ≠ 12

The average life expectancy of tires produced by the Whitney Tire Company has been 40,000 miles. Management believes that due to a new production process, the life expectancy of its tires has increased. In order to test the validity of this belief, the correct set of hypotheses is

H0: μ ≤ 40,000 Ha: μ > 40,000

The manager of an automobile dealership is considering a new bonus plan in order to increase sales. Currently, the mean sales rate per salesperson is five automobiles per month. The correct set of hypotheses for testing the effect of the bonus plan is

H0: μ ≤ 5 Ha: μ > 5

Other things being equal, compared to the paired-samples (or dependent) t-test, the independent t-test:

Has less power to find an effect.

A researcher measured a group of people's physiological reactions while watching horror films and compared them to when watching comedy films. The resulting data were normally distributed. What test should be used to analyse the data?

Paired-samples (dependent or related) t-test.

If you use a paired samples t-test:

The same participants take part in both experimental conditions. Other things being equal, you do not need as many participants as you would for an independent samples design.

Two samples of data are collected and the sample means calculated. If the samples come from the same population, then:

Their means should be roughly equal.

If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2, the

alternative hypothesis should state P1 - P2 > 0

n = 36 H0: μ ≤ 20 x = 24.6 Ha: μ > 20 σ = 12 Refer to Exhibit 9-1. If the test is done at a .05 level of significance, the null hypothesis should

be rejected

Exhibit 8-3 A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph. Refer to Exhibit 8-3. If the sample size was 25 (other factors remain unchanged), the interval for μ would

become wider

For a two-tailed test with a sample size of 40, the null hypothesis will not be rejected at a 5% level of significance if the test statistic is

between -1.96 and 1.96, exclusively

For a one-tailed test (upper tail) with a sample size of 900, the null hypothesis will be rejected at the .05 level of significance if the test statistic is

greater than or equal to 1.645

When the rejection region is in the lower tail of the sampling distribution, the p-value is the area under the curve

less than or equal to the test statistic

If the cost of a Type I error is high, a smaller value should be chosen for the

level of significance

Exhibit 9-6 A random sample of 100 people was taken. Eighty of the people in the sample favored Candidate A. We are interested in determining whether or not the proportion of the population in favor of Candidate A is significantly more than 75%. Refer to Exhibit 9-6. At a .05 level of significance, it can be concluded that the proportion of the population in favor of candidate A is

not significantly greater than 75%

Two approaches to drawing a conclusion in a hypothesis test are

p-value and critical value

When the p-value is used for hypothesis testing, the null hypothesis is rejected if

p-value ≤ α

A two-tailed test is performed at a 5% level of significance. The p-value is determined to be 0.09. The null hypothesis

should not be rejected

Exhibit 9-2 The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. Refer to Exhibit 9-2. At a .05 level of significance, it can be concluded that the mean of the population is

significantly greater than 3

If we calculated an effect size and found it was r = .21 which expression would best describe the size of effect? (Hint: The value of r can lie between 0 (no effect) and 1 (a perfect effect).)

small to medium

In developing an interval estimate of the population mean, if the population standard deviation is unknown

the sample standard deviation and t distribution can be used

In order to determine whether or not there is a significant difference between the hourly wages of two companies, the following data have been accumulated. Company 1 Company 2 n1 = 80 n2 = 60 = $10.80 = = $10.00 = $2.00 = $1.50 Refer to Exhibit 10-13. The null hypothesis for this test is

μ1 - μ2 = 0