- A juice drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of drink on an average. Any overfilling or under-filling results in the shutdown and readjustment of the machine. To determine whether or not the machine is properly adjusted, the correct set of the hypotheses is H0: μ = 12 Ha: μ ≠ 12
- A random sample of 100 people was taken. Eighty-five 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 80%. The test statistic is 1.25
- A random sample of 49 statistics examinations was taken. The average score, in the sample, was 84 with a variance of 12.25. The 95% confidence interval for the average examination score of the population of the examination is 82.99 to 85.01
- A sample of 225 elements from a population with a standard deviation of 75 is selected. The sample mean is 180. The 95% confidence interval for μ is 170.2 to 189.8
- A sample of 75 information systems managers had an average hourly income of $40.75 with a standard deviation of $7.00. The 95% confidence interval for the average hourly wage (in $) of all information system managers is 39.14 to 42.36
- A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. Any over filling or under filling 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
- As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution becomes smaller
- Exhibit 9-1
n = 36 = 24.6S = 12H0: μ ≤ 20 Ha: μ > 20
Refer to Exhibit 9-1. The test statistic is 2.3 - Exhibit 9-1
n = 36 = 24.6S = 12H0: μ ≤ 20 Ha: μ > 20
Refer to Exhibit 9-1. If the test is done at 95% confidence, the null hypothesis should be rejected - Exhibit 9-2
n = 64 = 50s = 16H0: μ ≥ 54 Ha: μ < 54
Refer to Exhibit 9-2. The test statistic equals -2 - Exhibit 9-3
n = 49 = 54.8s = 28H0: μ ≤ 50 Ha: μ > 50
Refer to Exhibit 9-3. The test statistic is 1.2 - Exhibit 9-5A random sample of 100 people was taken. Eighty-five 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 80%.
Refer to Exhibit 9-5. The test statistic is 1.25 - Exhibit 9-7A random sample of 16 statistics examinations from a large population was taken. The average score in the sample was 78.6 with a variance of 64. We are interested in determining whether the average grade of the population is significantly more than 75. Assume the distribution of the population of grades is normal.
Refer to Exhibit 9-7. At 95% confidence, it can be concluded that the average grade of the population is significantly greater than 75 - Exhibit 9-8The average gasoline price of one of the major oil companies in Europe has been $1.25 per liter. Recently, the company has undertaken several efficiency measures in order to reduce prices. Management is interested in determining whether their efficiency measures have actually reduced prices. A random sample of 49 of their gas stations is selected and the average price is determined to be $1.20 per liter. Furthermore, assume that the standard deviation of the population (σ) is $0.14.
Refer to Exhibit 9-8. Thep-value for this problem is 0.0062 - Exhibit 9-9The sales of a grocery store had an average of $8,000 per day. The store introduced several advertising campaigns in order to increase sales. To determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 64 days of sales was selected. It was found that the average was $8,300 per day. From past information, it is known that the standard deviation of the population is $1,200.
Refer to Exhibit 9-9. The correct null hypothesis for this problem is μ ≤ 8000 - For a lower tail test, the test statistics z is determined to be zero. The p-value for this test is +.5
- For a one-tailed (upper tail) hypothesis test with a sample size of 18 and a .05 level of significance, the critical value of the test statistic t is 1.734
- For a one-tailed hypothesis test (upper tail) the p-value is computed to be 0.034. If the test is being conducted at 95% confidence, the null hypothesis is rejected
- For a one-tailed hypothesis test (upper tail), the p-value is computed to be .034. If the test is being conducted at the 5% level of significance, the null hypothesis is rejected
- For a one-tailed test (upper tail) at 93.7% confidence, Z = -1.53
- From a population with a variance of 900, a sample of 225 items is selected. At 95% confidence, the margin of error is 3.92
- If the null hypothesis is ejected at the .05 level of significance, it will always be rejected at the .10 level of significance.
- In a two-tailed hypothesis test, the area in each tail corresponding to the critical values is equal to 1-α/2
- In developing a interval estimate, if the population standard deviation is unknown the sample standard deviation must be used.
- In hypothesis testing, the smaller the Type I error, the larger the Type II error will be
- In hypothesis testing, if the null hypothesis has been rejected when the alternative hypothesis has been true the correct decision has been made.
- In hypothesis testing, the critical value is a number that establishes the boundary of the rejection region
- In hypothesis testing, the tentative assumption about the population parameter is the null hypothesis.
- In interval estimation, as the sample size becomes larger, the interval estimate becomes narrower
- In order to estimate the average electric usage per month, a sample of 81 houses was selected ad the electric usage was determined. Assume a population standard deviation of 450 kilowatt-hours. If the sample mean is 1858 kWh, the 95% confidence interval estimate of the population mean is 160 to 1956 kWh
- 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 .75 Ha: p > .75
- 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
- Read the t statistics from the t distribution table and circle the correct answer. For a one-tailed test (upper tail), using a sample size of 18, and at the 5% level of significance, t= 1.740
- The average manufacturing work week in metropolitan Chattanooga was 40.1 hours last year. It is believed that the recession has led to a reduction in the average work week. To test the validity of this belief, the hypotheses are H0: μ ≥ 40.1 Ha: μ < 40.1
- The average monthly rent for one-bedroom apartments in Chattanooga has been $700. Because of the downturn in the real estate market, it is believed that there has been a decrease in the average rental. The correct hypotheses to be tested are H0: μ ≥ 700 Ha: μ < 700
- The critical value of t for a one-tailed test with 6 degrees of freedom using α =.05 is 2.447
- The level of significance is (1 – confidence level)
- The level of significance is the maximum allowable probability of Type I error
- The level of significance is the maximum allowable probability of Type I error
- 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
- the p-value must be a number between zero and one
- The p-value is a probability that measures the support (or lack of support) for the null hypothesis
- The p-value must be a number between zero and one
- The sample size needed to provide a margin of error of 2 or less with .95 probability when the population standard deviation equals 11 is 116
- The school’s newspaper reported that the proportion of students majoring in business is at least 30%. You plan on taking a sample to test the newspaper’s claim. The correct set of hypotheses is H0: P ≥ 0.30 Ha: P < 0.30
- When s is used to estimate σ, the margin of error is computed by using the t distribution
- When the following hypotheses are being tested at a level of significance of αH0: μ ≥ 500Ha: μ < 500the null hypothesis will be rejected if the p-value is ≤ α
- When the p-value is used for hypothesis testing, the null hypothesis is rejected if p-value ≤ α
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