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Statistics Test 3 Ch. 10-12
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Terms in this set (25)
Consider the value of t such that 0.025 of the area under the curve is to the left of t.
Step 1. Select the graph which best represents the given description of t.
Step 2. Assuming the degrees of freedom equals 10, select the t value from the t table.
Answer: ____________________
(1)
Step 1: Graph B
Step 2: -2.2281389 (B4; Left Tail)
An environmentalist wants to find out the fraction of oil tankers that have spills each month.
Step 1. Suppose a sample of 202 tankers is drawn. Of these ships, 56 had spills. Using the data, estimate the proportion of oil tankers that had spills. Enter your answer as a fraction or a decimal number rounded to three decimal places.
Answer: ____________________
Step 2. Suppose a sample of 202 tankers is drawn. Of these ships, 56 had spills. Using the data, construct the 80% confidence interval for the population proportion of oil tankers that have spills each month. Round your answers to three decimal places.
Answer: Lower endpoint: Upper endpoint:
(2)
Step 1: 0.277 (B9)
Step 2: (Lower = 0.2368651; Upper = 0.3175904)
In a sample of 64 cabinets, the average height was found to be 37.3 in. with a variance of 0.7.
Give a point estimate for the population standard deviation of the height of the cabinets. Round your answer to two decimal places, if necessary.
Answer: ____________________
(3)
0.84 (C19)
Given two independent random samples with the following results:
n_1 = 9
x ̅_1 = 131
s_1 = 30
n_2 = 10
x ̅_2 = 162
s_2 = 33
Use this data to find the 95% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed.
Step 1. Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Step 2. Find the standard error of the sampling distribution to be used in constructing the confidence interval. Round your answer to the nearest whole number.
Step 3. Construct the 95% confidence interval. Round your answers to the nearest whole number.
Answer: Lower endpoint:
Upper endpoint:
(4)
Step 1: 2.11 (I26)
Step 2: 15 (D28)
Step 3: (Lower = 61.655811; Upper = 0.3441888)
Given two dependent random samples with the following results:
Population 1: 25, 32, 32, 27, 27, 36, 43
Population 2: 17, 26, 26, 41, 35, 42, 28
Use this data to find the 80% confidence interval for the true difference between the population means. Assume that both populations are normally distributed.
Step 1. Find the point estimate for the population mean of the paired differences. Let x_1 be the value from Population 1 and x_2 be the value from Population 2 and use the formula 〖d = x〗_2 〖 - x〗_1 to calculate the paired differences. Round your answer to one decimal place.
Step 2. Calculate the sample standard deviation of the paired differences. Round your answer to six decimal places.
Step 3. Calculate the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.
Step 4. Construct the 80% confidence interval. Round your answers to one decimal place.
Answer: Lower endpoint: Upper endpoint:
A34 (5)
Step 1: -1 (K37)
Step 2: 10.40833 (L40)
Step 3: 5.6639688 (B41)
Step 4: (Lower = -6.6639688; Upper = 4.6639688)
A state legislator wants to determine whether his voters' performance rating (0 - 100) has changed from last year to this year. The following table shows the legislator's performance from the same ten randomly selected voters for last year and this year. Use this data to find the 98% confidence interval for the true difference between the population means. Assume that the populations of voters' performance ratings are normally distributed for both this year and last year.
Rating (last year): 74, 83, 91, 65, 55, 55, 85, 55, 93, 63
Rating (this year): 46, 60, 82, 77, 47, 80, 78, 80, 91, 76
Step 1. Find the point estimate for the population mean of the paired differences. Let x_1 be the rating from last year and x_2 be the rating from this year and use the formula 〖d = x〗_2 〖 - x〗_1 to calculate the paired differences. Round your answer to one decimal place.
Step 2. Calculate the sample standard deviation of the paired differences. Round your answer to six decimal places.
Step 3. Calculate the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.
Step 4. Construct the 98% confidence interval. Round your answers to one decimal place.
Answer: Lower endpoint: Upper endpoint:
A45 (6)
Step 1: -0.2
Step 2: 18.4...
Step 3: 16.488188
Step 4: (Lower = -16.688188; Upper = 16.288188)
A telephone service representative believes that the proportion of customers completely satisfied with their local telephone service is different between the Midwest and the Northeast. The representative's belief is based on the results of a survey. The survey included a random sample of 1400 midwestern residents and 1320 northeastern residents. 50% of the midwestern residents and 38% of the northeastern residents reported that they were completely satisfied with their local telephone service. Find the 98% confidence interval for the difference in two proportions.
Step 1. Find the critical value that should be used in constructing the confidence interval.
Step 2. Find the value of the standard error. Round your answer to three decimal places.
Step 3. Construct the 98% confidence interval. Round your answers to three decimal places.
A56 (7)
Step 1: 2.3263479
Step 2: 0.188959
Step 3: (Lower = 0.0760415; Upper = 0.163958)
Construct the confidence interval for the ratio of the population variances given the following sample statistics. Round your answers to four decimal places.
n_1 = 12, n_2 = 9, □(□(〖s_1〗^2/〖s_2〗^2 )) = 1.91, α = 0.05
Answer: Lower endpoint:
Upper endpoint:
A70 (8)
Lower = 0.2772939
Upper = 4.2435014
Find the best point estimate for the ratio of the population variances given the following sample statistics. Round your answer to four decimal places.
n_1 = 23, n_2 = 29, 〖s_1〗^2 = 71.195, 〖s_2〗^2 = 64.723
A80 (9)
1.099995365
The mayor of a town believes that over 20% of the residents favor construction of a new bridge. Is there sufficient evidence at the 0.10 level to support the mayor's claim? After information is gathered from 230 voters and a hypothesis test is completed, the mayor fails to reject the null hypothesis at the 0.10 level.
What is the conclusion regarding the mayor's claim?
A) There is sufficient evidence at the 0.10 level of significance that the percentage of residents who support the construction is over 20%.
B) There is not sufficient evidence at the 0.10 level of significance that the percentage of residents who support the construction is over 20%.
A84 (10)
B) There is not sufficient evidence at the 0.10 level of significance that the percentage of residents who support the construction is over 20%.
The director of research and development is testing a new medicine. She wants to know if there is evidence at the 0.02 level that the medicine relieves pain in less than 376 seconds. For a sample of 76 patients, the mean time in which the medicine relieved pain was 373 seconds. Assume the standard deviation is known to be 21.
State the null and alternative hypotheses for the above scenario.
Answer: H_0:
H_a:
(11)
H_0: mean is > or = to 376
H_a: mean is < 376
Using traditional methods it takes 92 hours to receive an advanced driving license. A new training technique using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique on 60 students and observed that they had a mean of 94 hours. Assume the population variance is known to be 49. Is there evidence at the 0.1 level that the technique lengthens the training time?
Step 1. State the null and alternative hypotheses.
Answer: H_0:
H_a:
Step 2. Find the value of the test statistic. Round your answer to two decimal places.
Answer: ____________________
Step 3. Specify if the test is one-tailed or two-tailed.
A) One-Tailed Test
B) Two-Tailed Test
Step 4. Find the P-value of the test statistic. Round your answer to four decimal places.
Answer: ____________________
Step 5. Identify the level of significance for the hypothesis test.
Answer: ____________________
Step 6. Make the decision to reject or fail to reject the null hypothesis.
A) Reject Null Hypothesis
B) Fail to Reject Null Hypothesis
A90 (12)
Step 1: H_0: mean is < or = to 92; H_a: mean > 92
Step 2: 2.2131333
Step 3: A) One-Tailed TEst
Step 4: 0.0136
Step 5: 0.1
Step 6: A) Reject Null Hypothesis
A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 438 gram setting. It is believed that the machine is underfilling or overfilling the bags. A 20 bag sample had a mean of 432 grams with a variance of 144. Assume the population is normally distributed. A level of significance of 0.02 will be used. Specify the type of hypothesis test.
A) Left-Tailed Test
B) Right-Tailed Test
C) Two-Tailed Test
A107 (13)
C) Two-Tailed Test
Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 4.6 parts/million (ppm). A researcher believes that the current ozone level is at an excess level. The mean of 27 samples is 5.0 ppm with a variance of 1.21. Does the data support the claim at the 0.01 level? Assume the population distribution is approximately normal.
Step 1. State the null and alternative hypotheses.
Answer: H_0: H_a:
Step 2. Find the value of the test statistic. Round your answer to three decimal places.
Answer: ____________________
Step 3. Specify if the test is one-tailed or two-tailed.
A) One-Tailed Test
B) Two-Tailed Test
Step 4. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.
Answer: Reject H_0 if t>
Step 5. Make the decision to reject or fail to reject the null hypothesis.
A) Reject Null Hypothesis
B) Fail to Reject Null Hypothesis
A109 (14)
Step 1: H_0: < or = to 4.6; H_a: > 4.6
Step 2: 1.88951
Step 3: A) One-Tailed Test
Step 4: 2.4786295
Step 5: B) Fail to Reject Null Hypothesis
The mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 1300 voters in the town and found that 54% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is over 51%. Testing at the 0.05 level, is there enough evidence to support the strategist's claim?
Step 1. State the null and alternative hypotheses.
Answer: H_0: H_a:
Step 2. Find the value of the test statistic. Round your answer to two decimal places.
Step 3. Specify if the test is one-tailed or two-tailed.
A) One-Tailed Test
B) Two-Tailed Test
Step 4. Determine the P-value of the test statistic. Round your answer to four decimal places.
Step 5. Identify the value of the level of significance.
Answer: ____________________
Step 6. Make the decision to reject or fail to reject the null hypothesis.
A) Reject Null Hypothesis
B) Fail to Reject Null Hypothesis
Step 7. State the conclusion of the hypothesis test.
A) There is sufficient evidence to support the claim that the percentage of residents who favor construction is over 51%.
B) There is not sufficient evidence to support the claim that the percentage of residents who favor construction is over 51%.
A122 (15)
Step 1: H_0: mean < or = 0.51 H_a: mean > 0.51
Step 2: 2.16
Step 3: A) One-Tailed Test
Step 4: 0.0152
Step 5: 0.05
Step 6: A) Reject Null Hypothesis
Step 7: A) Ther is sufficient evidence to support the claim that the percentage of residents who favor construction is over 51%
A geologist examines 14 water samples for potassium chloride concentration. The mean potassium chloride concentration for the sample data is 0.553 cc/cubic meter with a standard deviation of 0.0052. Determine the 98% confidence interval for the population mean potassium chloride concentration. Assume the population is approximately normal.
Step 1. Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer: ____________________
Step 2. Construct the 98% confidence interval. Round your answer to three decimal places.
Answer: Lower endpoint:
Upper endpoint:
A176 or A170 (17)
Step 1: 2.650
Step 2: (Lower = 0.5493167; Upper = 0.5566833)
NASA is conducting an experiment to find out the fraction of people who black out at G forces greater than 6.
Step 1. Suppose a sample of 256 people is drawn. Of these people, 152 didn't pass out at G forces greater than 6. Using the data, estimate the proportion of people who pass out at more than 6 Gs. Enter your answer as a fraction or a decimal number rounded to three decimal places.
Answer: ____________________
Step 2. Suppose a sample of 256 people is drawn. Of these people, 152 didn't pass out. Using the data, construct the 80% confidence interval for the population proportion of people who black out at G forces greater than 6. Round your answers to three decimal places.
Answer: Lower endpoint:
Upper endpoint:
A182 (18)
Step 1: 0.40625
Step 2: (Lower = 0.3669118; Upper = 0.4455882)
What is the best point estimate for the population's variance if the sample standard deviation is 4.6? Round your answer to one decimal place, if necessary.
Answer:
A194 (19)
Answer: 21.16
Find the point estimate for the true difference between the given population means. Round your answer to six decimal places.
Weights (in Grams) of Soap Bar A: 123, 124, 123, 124, 123, 123, 124, 125, 122, 124, 123
Weights (in Grams) of Soap Bar B: 125, 125, 123, 125, 125, 121, 124, 124, 126, 121, 120, 126, 122
Answer:
A197 (20)
Answer: -0.1608392
A research company desires to know the mean consumption of meat per week among males over age 49. A sample of 512 males over age 49 was drawn and the mean meat consumption was 4.2 pounds. Assume that the population standard deviation is known to be 1.2 pounds. Construct the 90% confidence interval for the mean consumption of meat among males over age 49. Round your answers to one decimal place.
Answer: Lower endpoint:
Upper endpoint:
A202 (21)
Lower: 4.1127685
Upper: 4.2872315
Consider the value of t such that 0.05 of the area under the curve is to the right of t.
Step 1. Select the graph which best represents the given description of t.
Step 2. Assuming the degrees of freedom equals 7, select the t value from the t table.
Answer:
A213 (22)
Step 1: A)
Step 2: 1.8945786
A manager records the repair cost for 17 randomly selected stereos. A sample mean of $82.37 and standard deviation of $19.66 are subsequently computed. Determine the 80% confidence interval for the mean repair cost for the stereos. Assume the population is approximately normal.
Step 1. Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer: ____________________
Step 2. Construct the 80% confidence interval. Round your answer to two decimal places.
Answer: Lower endpoint: Upper endpoint:
A219 (23)
Step 1: 1.3367572
Step 2: (Lower = 75.996007; Upper = 88.743993)
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level.
Step 1. Suppose a sample of 1123 tenth graders is drawn. Of the students sampled, 213 read at or below the eighth grade level. Using the data, estimate the proportion of tenth graders reading at or below the eighth grade level. Enter your answer as a fraction or a decimal number rounded to three decimal places.
Answer: ____________________
Step 2. Suppose a sample of 1123 tenth graders is drawn. Of the students sampled, 213 read at or below the eighth grade level. Using the data, construct the 90% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level. Round your answers to three decimal places.
Answer: Lower endpoint:
Upper endpoint:
A231 (24)
Step 1: 0.1896705
Step 2: (Lower = 0.1704277; Upper = 0.2089133)
A researcher compares the effectiveness of two different instructional methods for teaching physiology. A sample of 177 students using Method 1 produces a testing average of 84.2. A sample of 147 students using Method 2 produces a testing average of 58.2. Assume that the population standard deviation for Method 1 is 14.72, while the population standard deviation for Method 2 is 12.91. Determine the 90% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2.
Step 1. Find the critical value that should be used in constructing the confidence interval.
Answer: ____________________
Step 2. Construct the 90% confidence interval. Round your answers to one decimal place.
Answer: Lower endpoint:
Upper endpoint:
A243 (25)
Step 1: 1.645
Step 2: (Lower = 23.473991; Upper = 28.526009)
Find the point estimate for the true difference between the given population means. Round your answer to the nearest whole number.
x ̅_1 = 42 and x ̅_2 = 47
Answer:
A257 (26)
Answer: -5
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Verified questions
STATISTICS
Listed below are the numbers of deaths from lightning strikes in the United States each year for a sequence of 14 recent and consecutive years. Find the values of the indicated statistics. $$ \begin{array} { c c c c c c c c c c c c } { 51 } & { 44 } & { 51 } & { 43 } & { 32 } & { 38 } & { 48 } & { 45 } & { 27 } & { 34 } & { 29 } & { 26 } & { 28 } & { 23 } \end{array} $$ Median.
PROBABILITY
Four married couples have bought 8 seats in the same row for a concert. In how many different ways can they be seated (a) with no restrictions? (b) if each couple is to sit together? (c) if all the men sit together to the right of all the women? $$
PROBABILITY
The city of Cieansburg has 8325 registered voters. There is an election for mayor of Cieansburg, and there are three candidates for the position: Smith, Jones, and Brown. The day before the election a telephone poll of 680 randomly chosen registered voters produce the following results: 306 people surveyed indicated that they would vote for Smith, 272 indicated that they would vote for Jones and 102 indicated that they would vote for Brown. (a) Describe the population for this survey. (b) Describe the sample for this survey. (c) Name the sampling method used for this survey.
STATISTICS
To illustrate the effects of driving under the influence (DUI) of alcohol, a police officer brought a DUI simulator to a local high school. Student reaction time in an emergency was measured with unimpaired vision and also while wearing a pair of special goggles to simulate the effects of alcohol on vision. For a random sample of nine teenagers, the time (in seconds) required to bring the vehicle to a stop from a speed of 60 miles per hour was recorded. $$ \begin{matrix} \text{Subject} & \text{1} & \text{2} & \text{3} & \text{4} & \text{5} & \text{6} & \text{7} & \text{8} & \text{9}\\ \text{Normal, }{ X_i} & \text{4.47} & \text{4.24} & \text{4.58} & \text{4.65} & \text{4.31} & \text{4.80} & \text{4.55} & \text{5.00} & \text{4.79}\\ \text{Impaired, }{ Y_i} & \text{5.77} & \text{5.67} & \text{5.51} & \text{5.32} & \text{5.83} & \text{5.49} & \text{5.23} & \text{5.61} & \text{5.63}\\ \end{matrix} $$ (a) Whether the student had unimpaired vision or wore goggles first was randomly selected. Why is this a good idea in designing the experiment? (b) Use a 95% confidence interval to test if there is a difference in braking time with impaired vision and normal vision where the differences are computed as "impaired minus normal. "Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.