Stats Exam 4
What conditions are necessary in order to use the z-test to test the difference between two population means? Select all the necessary conditions below.
The samples must be randomly selected, Each population has a normal distribution with a known standard deviation, The samples must be independent.
Classify the two given samples as independent or dependent. Sample 1: The PSAT scores for 50 high school students Sample 2:The SAT scores for the same 50 high school students Choose the correct answer below.
The two given samples are dependent because the same students were sampled.
Classify the two given samples as independent or dependent. Sample 1: The test scores of 43 students who had less than eight hours of sleep the night prior to taking the test Sample 2: The test scores of 33 students who had at least eight hours of sleep the night prior to taking the test Choose the correct answer below.
The two given samples are independent because different students were sampled.
What conditions are necessary in order to use the z-test to test the difference between two population means?
The samples must be independent. Each population has a normal distribution with a known standard deviation. The samples must be randomly selected.
You are testing a claim and incorrectly use the normal sampling distribution instead of the t-sampling distribution. Does this make it more or less likely to reject the null hypothesis? Is this result the same no matter whether the test is left-tailed, right-tailed, or two-tailed? Explain your reasoning. (a)Is the null hypothesis more or less likely to be rejected? Explain. (b)Is the result the same?
(A)More likely;for degrees of freedom less than 30, the tail of the curve are thicker for a t-sampling distribution. Therefore, if you incorrectly use a standard normal sampling distribution, the area under the curve at the tails will be smaller than what it would be for the t-test, meaning the critical value(s) will lie closer to the mean. (b)The result is the same. In each case, the tail thickness affects the location of the critical value(s).
Determine whether a normal sampling distribution can be used for the following sample statistics. If it can be used, test the claim about the difference between two population proportions p1 and p2 at the level of significance α. Assume that the samples are random and independent. Claim: p1≠p2, α=0.01 Sample Statistics: x1=36, n1=65, x2=38, n2=75 (a)Determine whether a normal sampling distribution can be used.
(a)
Find the critical value(s) and rejection region(s) for the indicated t-test, level of significance α, and sample size n. Left-tailed test, α=0.025, n=28 (a)The critical value(s) is/are ___ (b)Determine the rejection region(s). Select the correct choice below and fill in the answer box(es) within your choice.
(a) -2.052 (use .025 and 27 in the t distribution table) (b)t<-2.052
Find the critical value(s) and rejection region(s) for the indicated t-test, level of significance α, and sample size n. Two-tailed test, α=0.10, n=5 (a)The critical value(s) is/are ____ (b)Determine the rejection region(s). Select the correct choice below and fill in the answer box(es) within your choice.
(a)-2.132, and 2.132 (use .10 and 4 in t distribution table(make sure to do two tailed test)) (b)t<- 2.132 and t>2.132
Find the critical value(s) and rejection region(s) for the indicated t-test, level of significance α, and sample size n. Right-tailed test, α=0.10, n=25 (a)The critical value(s) is/are ____ (b)Determine the rejection region(s). Select the correct choice below and fill in the answer box(es) within your choice.
(a)1.318 (use .10 and 24 in the t distribution table) (b)t>1.318
A research center claims that 28% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 1000 adults in that country, 31% say that they would travel into space on a commercial flight if they could afford it. At α=0.01, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. (a)Identify the claim and state H0 and Ha. (b)Let p be the population proportion of successes, where a success is an adult in the country who would travel into space on a commercial flight if they could afford it. State H0 and Ha. Select the correct choice below and fill in the answer boxes to complete your choice. (c)Use technology to find the P-value. Identify the standardized test statistic. Identify the P-value. (d)Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.
(a)28%of adults in the country would travel into space on a commercial flight if they could afford it. (b)H0:p=0.28 Ha:p≠0.28 (c)z=2.11 (use 1 prop z test) (P0=.27, x=348(.29x1200), n=1200) P=0.035 (d)Fail to reject the null hypothesis. There is not enough evidence to reject the research center's claim.
For the given data, (a) find the test statistic, (b) find the standardized test statistic, (c) decide whether the standardized test statistic is in the rejection region, and (d) decide whether you should reject or fail to reject the null hypothesis. The samples are random and independent. Claim: μ1<μ2, α=0.01. Sample statistics: x1=1230, n1=50, x2=1200, and n2=80. Population statistics: σ1=70 and σ2=115 (a) The test statistic for μ1−μ2 is _______. (b)The standardized test statistic for μ1−μ2 is ______ (c) Is the standardized test statistic in the rejection region? (d)Should you reject or fail to reject the null hypothesis?
(a)30 (1230-1200) (b) The standardized test statistic for μ1−μ2 is 1.85 use 2 sample z test (c)No (d)H0:μ1≥μ2; Ha:μ1<μ2. Fail to reject H0. At the1% significancelevel, there is not enough evidence to support the claim.
Describe type I and type II errors for a hypothesis test of the indicated claim. A shoe store claims that at least 60% of its new customers will return to buy their next pair of shoes. (a)Describe the type I error. Choose the correct answer below (b)Describe the type II error. Choose the correct answer below.
(a)A type I error will occur when the actual proportion of new customers who return to buy their next article of clothing is no more than 0.60, but you reject H0: p≤0.60. (b)A type II error will occur when the actual proportion of new customers who return to buy their next article of clothing is more than 0.60, but you fail to reject H0:p≤0.60.
State whether the standardized test statistic t indicates that you should reject the null hypothesis. Explain. (left tailed) (a) t=2.153 (b) t=0 (c) t=−2.041 (d) t=-2.163
(a)Fail to reject H0,because t>−2.113. (b)Fail to reject H0, because t>−2.113. (c)Fail to reject H0,because t>−2.113. (d)Reject H0,because t<−2.113.
The P-value for a hypothesis test is shown. Use the P-value to decide whether to reject H0 when the level of significance is (a) α=0.01, (b) α=0.05, and (c) α=0.10. P=0.0618 (a)Do you reject or fail to reject Ho at the 0.01 level of significance? (b)Do you reject or fail to reject Ho at the 0.05 level of significance? (c)Do you reject or fail to reject Ho at the 0.10 level of significance?
(a)Fail to reject Ho because theP-value, 0.0618, is greater than α=0.01. (b).Fail to reject Ho because the P-value, 0.0618, is greater than α=0.05. (c)Reject Ho because theP-value, 0.0618,is less than α=0.10.
The P-value for a hypothesis test is shown. Use the P-value to decide whether to reject H0 when the level of significance is (a) α=0.01, (b) α=0.05, and (c) α=0.10. P=0.0618 (a)Do you reject or fail to reject Ho at the 0.01 level of significance? (b)Do you reject or fail to reject Ho at the 0.05 level of significance? (c)Do you reject or fail to reject Ho at the 0.10 level of significance?
(a)Fail to reject Ho because theP-value, 0.0618, is greater than α=0.01. (b)Fail to reject Ho because theP-value, 0.0618, is greater than α=0.05. (c)Reject Ho because theP-value, 0.0618,is less than α=0.10.
An oceanographer claims that the mean dive duration of a North Atlantic right whale is 11.7 minutes. A random sample of 36 dive durations has a mean of 12.4 minutes and a standard deviation of 2.2 minutes. At α=0.05 is there enough evidence to reject the oceanographer's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. (a)Identify the claim and state H0 and Ha. (b)Use technology to find the P-value. Find the standardized test statistic, t. (c)Decide whether to reject or fail to reject the null hypothesis. (d)Interpret the decision in the context of the original claim.
(a)H0:μ=11.7 Ha:μ≠11.7 (b)t=1.91 p=.064 (c)Fail to reject H0 because theP-value is greater than α. (d)There is not enough evidence at the 5% level of significance to reject the claim that the mean dive duration of a North Atlantic right whale is equal to 11.7 minutes.
A consumer group claims that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.7 seconds. A random sample of 22 sedans has a mean minimum time to travel a quarter mile of 15.4 seconds and a standard deviation of 2.11 seconds. At α=0.05 is there enough evidence to support the consumer group's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. (a)Identify the claim and state H0 and Ha. (b)Use technology to find the P-value. Find the standardized test statistic, t. (c)Decide whether to reject or fail to reject the null hypothesis. (d)Interpret the decision in the context of the original claim.
(a)H0:μ≤14.7 Ha:μ>14.7 (b)t=1.56 p=.067 use t test (c)Fail to reject H0 because the P-value is greater than α. (d)There is not enough evidence at the 55% level of significance to support the claim that the mean minimum time it takes for a sedan to travel a quarter mile is greater than 14.7 seconds.
Test the claim about the population mean μ at the level of significance α. Assume the population is normally distributed. Claim: μ<5215; α=0.01 Sample statistics: x=5317, s=5949, n=53 (a)What are the null and alternative hypotheses? (b)Find the standardized test statistic t.
(a)H0:μ≥5215 Ha:μ<5215 (b).13 (c).549 plug into t test on calculator (d) Fail to reject H0. There is not enough evidence at the 11% level of significance to support the claim.
A random sample of 88 eighth grade students' scores on a national mathematics assessment test has a mean score of 294. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 285. Assume that the population standard deviation is 33. At α=0.05, is there enough evidence to support the administrator's claim? Complete parts (a) through (e). (a) Write the claim mathematically and identify H0 and Ha. Choose the correct answer below.
(a)H0: μ≤285 Ha: μ>285 (claim)
You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 33 students. You want to test this claim. You randomly select 18 classes taught by full-time faculty and determine the class size of each. The results are shown in the table below. At α=0.10, can you support the university's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. (a)Write the claim mathematically and identify H0 and Ha. Which of the following correctly states H0 and Ha? (b)Use technology to find the P-value. (c)Decide whether to reject or fail to reject the null hypothesis. Which of the following is correct? (d)Interpret the decision in the context of the original claim.
(a)H0: μ≥33 Ha:μ<33 (b)enter list into L1 and then use t test with data P=. 012 (c)Reject H0 because theP-value is less than the significance level. (d)At the 10% level of significance, there is sufficient evidence to support the claim that the mean class size for full-time faculty is fewer than 33 students.
Test the claim about the difference between two population means μ1 and μ2 at the level of significance α. Assume the samples are random and independent, and the populations are normally distributed. Claim: μ1=μ2; α=0.01. Assume σ21=σ22 Sample statistics: x1=31.6, s1=3.6, n1=14 and x2=34.6, s2=2.2, n2=17 (a)Identify the null and alternative hypotheses. Choose the correct answer below. (b)Find the standardized test statistic t. (c)Find the P-value. (d)Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.
(a)H0:μ1=μ2 Ha:μ1≠μ2 (b)t=-2.85 use 2 samp t test (make sure pooled yes) (c)p=.008 (d)Reject H0. There is enough evidence at the 1% level of significance to reject the claim.
Test the claim about the difference between two population means μ1 and μ2 at the level of significance α. Assume the samples are random and independent, and the populations are normally distributed. Claim: μ1≤μ2; α=0.10. Assume σ21≠σ22 Sample statistics: x1=2414, s1=170, n1=12 and x2=2292, s2=52, n2=9 (a)Identify the null and alternative hypotheses. Choose the correct answer below. (b)Find the standardized test statistic t. (c)Find the P-value. (d)Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.
(a)H0:μ1≤μ2 Ha:μ1>μ2 (b)t=2.34 use 2 samp t test (make sure pooled no) (c)P=. 017 (d)Reject H0. There is enough evidence at the 10% level of significance to reject the claim.
The lengths of time (in years) it took a random sample of 32 former smokers to quit smoking permanently are listed. Assume the population standard deviation is 4.5years. At α=0.02, is there enough evidence to reject the claim that the mean time it takes smokers to quit smoking permanently is 13 years? Complete parts (a) through (e). (a) Identify the claim and state the null hypothesis and alternative hypothesis. (b) Identify the standardized test statistic. Use technology.
(a)H0:μ=13(claim) Ha:μ≠13 (b)
Use a t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. Assume the population is normally distributed. Claim: μ≠26; α=0.05 Sample statistics: x=21.1, s=5.1, n=12 (a)What are the null and alternative hypotheses? Choose the correct answer below. (b)What is the value of the standardized test statistic? (c)What is the P-value of the test statistic? (d)Decide whether to reject or fail to reject the null hypothesis.
(a)H0:μ=26 Ha:μ≠26 (b)-3.33 21.1-26/ 5.1/ square root of 12 (c).007 (use 2 tailed!!) use https://www.socscistatistics.com/pvalues/tdistribution.aspx (d)Reject H0. There is enough evidence to support the claim.
A nutritionist claims that the mean tuna consumption by a person is 3.4 pounds per year. A sample of 60 people shows that the mean tuna consumption by a person is 3.2 pounds per year. Assume the population standard deviation is 1.21 pounds. At α=0.1,can you reject the claim? (a)Identify the null hypothesis and alternative hypothesis. (b)Identify the standardized test statistic. (c) Find the P-value. (d) Decide whether to reject or fail to reject the null hypothesis.
(a)H0:μ=3.4 Ha:μ≠3.4 (b)-1.28 3.2-3.4/ 1.21/square root of 60 (c)use https://www.zscorecalculator.com/ to find the area to the left =.100 Times that by 2 2 (d)Fail to reject H0. There is not sufficient evidence to reject the claim that mean tuna consumption is equal to 3.4 pounds.
Use a t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. Assume the population is normally distributed. Claim: μ=51,100; α=0.10 Sample statistics: x=51,151, s=2600, n=15 (a)What are the null and alternative hypotheses? Choose the correct answer below. (b)What is the value of the standardized test statistic? (c)What is(are) the critical value(s)? (d)Decide whether to reject or fail to reject the null hypothesis.
(a)H0:μ=51,100 Ha:μ≠51,100 (b).08 51151-51100/ 2600/ square root of 15 (c)1.761 and -1.761 use .10 and 14 in t distribution table (make sure 2-test) (d)Fail to reject H0. There is not enough evidence to reject the claim.
A random sample of 88 eighth grade students' scores on a national mathematics assessment test has a mean score of 294. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 285.Assume that the population standard deviation is 33.At α=0.05, is there enough evidence to support the administrator's claim? (a)Write the claim mathematically and identify H0 and Ha. Choose the correct answer below. (b)Find the standardized test statistic z, and its corresponding area. (c)Find the P-value. (d)Decide whether to reject or fail to reject the null hypothesis. (e)Interpret your decision in the context of the original claim.
(a)H0:μ≤285 Ha:μ>285(claim) (b)z=2.56 294-286/33/square root of 88 (c).005 find the z score corresponding to 2.56=.9948 1-.9948=.005 (d)Reject H0 (e)At the 5% significance level, there is enough evidence to support the administrator's claim that the mean score for the state's eighth graders on the exam is more than 285.
Use technology and a t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. Assume the population is normally distributed. Claim: μ>70; α=0.01 Sample statistics: x=70.9, s=3.1, n=27 (a)What are the null and alternative hypotheses? Choose the correct answer below. (b)What is the value of the standardized test statistic? (c)What is the P-value of the test statistic? (d)Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below.
(a)H0:μ≤70 HA:μ>70 (b)1.51 70.9-70/ 3.1/square root of 27 (c).072 use https://www.socscistatistics.com/pvalues/tdistribution.aspx (d)Fail to reject H0. There is not enough evidence to support the claim.
Use a t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. Assume the population is normally distributed. Claim: μ≥7800; α=0.01 Sample statistics: x=7600, s=480, n=20 (a)What are the null and alternative hypotheses? (b)What is the value of the standardized test statistic? (c)What is the P-value? (d)Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below.
(a)H0:μ≥7800 Ha:μ<7800 (b)-1.86 7600-7800/ 480/square root of 20 (c).039 use https://www.socscistatistics.com/pvalues/tdistribution.aspx (d)Fail to reject H0. At the 1% level of significance, there is not enough evidence to reject the claim.
Test the claim about the difference between two population means μ1 and μ2 at the level of significance α. Assume the samples are random and independent, and the populations are normally distributed. Claim: μ1=μ2; α=0.01 Population statistics: σ1=3.4, σ2=1.6 Sample statistics: x1=17, n1=31, x2=15, n2=28 (a)Determine the alternative hypothesis. (b)Determine the standardized test statistic. (c)Determine the P-value. (d)What is the proper decision?
(a)Ha:μ1≠u2 (b)z=2.94 use 2-samp z test (c).003 use 2 samp z test (d)Reject H0. There is enough evidence at the 1% level of significance to reject the claim.
Explain how to find the critical values for a t-distribution. (a)Give the first step. Choose the correct answer below. (b)If the hypothesis test is left-tailed, use the _____ column with a _____sign. (c)If the hypothesis test is right-tailed, use the ____ column with a ____sign. (d)If the hypothesis test is two-tailed, use the ____ column with a ___sign.
(a)Identify the level of significance α and the degrees of freedom, d.f.=n−1 (b)One tail, α & negative (c)One tail, α & positive (d)Two tails, α & negative and a positive
A humane society claims that less than 73% of households in a certain country own a pet. In a random sample of 400 households in that country, 276 say they own a pet. At α=0.01, is there enough evidence to support the society's claim? Complete parts (a) through (c) below. (a) Identify the claim and state H0 and Ha. Let p be the population proportion of successes, where a success is a household in the country that owns a pet. State H0 and Ha. (b) Use technology to find the P-value. Identify the standardized test statistic. Identify the P-value. (c) Decide whether to reject or fail to reject the null hypothesis and (d) interpret the decision in the context of the original claim.
(a)Less than 73% of households in the country own a pet. H0:p≥. 73 Ha:p<. 73 (b) use 1 prop z test (P0=.73, x=276, n=400) z=- 1.80 p=.036 (c)Fail to reject the null hypothesis. There is not enough evidence to support the society's claim.
Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion p at the given level of significance α using the given sample statistics. Claim: p<0.12; α=0.05; Sample statistics: p=0.08, n=25 (a)Can the normal sampling distribution be used? (b)State the null and alternative hypotheses. Choose the correct answer below. (c)Determine the critical value(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (d)Find the z-test statistic. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (e)What is the result of the test?
(a)No, because np is less than 5. (b)The test cannot be performed. (c)The test cannot be performed. (d)The test cannot be performed. (e)The test cannot be performed
State whether the standardized test statistic t indicates that you should reject the null hypothesis. Explain.(two tailed) (a) t=−2.041 (b) t=1.897 (c) t=2.055 (d) t=-1.962
(a)Reject H0, because t<−1.962. (b)Fail to reject H0,because −1.962<t<1.962. (c)Reject H0, because t>1.962. (d)Reject H0,because t<−1.962.
State whether the standardized test statistic t indicates that you should reject the null hypothesis. Explain.(right tailed) (a) t=1.678 (b) t=0 (c) t=1.566 (d) t=-1.685
(a)Reject H0, because t>1.597. (b)Fail to reject H0, because t<1.597. (c)Fail to reject H0, because t<1.597. (d)Fail to reject H0, because t<1.597.
Identify the type I error and the type II error for a hypothesis test of the indicated claim. The percentage of high school students who graduate is equal to 55%. (a)Identify the type I error. Choose the correct answer below. (b)Identify the type II error. Choose the correct answer below.
(a)Reject the null hypothesis that the percentage of high school students who graduate is equal to 55% when it is actually true. (b)Fail to reject the null hypothesis that the percentage of high school students who graduate is equal to 55% when it is actually false.
Determine whether the claim stated below represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that (a) rejects the null hypothesis or (b) fails to reject the null hypothesis? A report claims that at most 83% of households in a specific county struggle to afford basic necessities. (a)Does the claim represent the null hypothesis or the alternative hypothesis? (b)How should you interpret a decision that rejects the null hypothesis? (c)How should you interpret a decision that fails to reject the null hypothesis?
(a)Since the claim contains a statement of equality, it represents the null hypothesis. (b)There is enough evidence to reject the claim that at most 83% of households in a county struggle to afford basic necessities. (c)There is not enough evidence to reject the claim that at most 83%of households in a county struggle to afford basic necessities.
Determine whether the claim stated below represents the null hypothesis or the alternative hypothesis. If a hypothesis test is performed, how should you interpret a decision that (a) rejects the null hypothesis or (b) fails to reject the null hypothesis? A scientist claims that the mean incubation period for the eggs of a species of bird is more than 47 days. (a)Does the claim represent the null hypothesis or the alternative hypothesis? (b)How should you interpret a decision that rejects the null hypothesis? (c)How should you interpret a decision that fails to reject the null hypothesis?
(a)Since the claim does not contain a statement of equality, it represents the alternative hypothesis. (b)There is sufficient evidence to support the claim that the mean incubation period for the eggs of a species of bird is more than 47 days. (c)There is insufficient evidence to support the claim that the mean incubation period for the eggs of a species of bird is more than 47 days.
(a)What does the symbol d bar represent? (b)What does the symbol sd represent?
(a)The mean of the differences between the paired data entries in the dependent samples (b)The standard deviation of the differences between the paired data entries in the dependent samples
A car company says that the mean gas mileage for its luxury sedan is at least 24 miles per gallon (mpg). You believe the claim is incorrect and find that a random sample of 8 cars has a mean gas mileage of 22 mpg and a standard deviation of 2 mpg. At α=0.05, test the company's claim. Assume the population is normally distributed. (a)Which sampling distribution should be used and why? (b)State the appropriate hypotheses to test. (c)What is the value of the standardized test statistic? (d)What is the critical value? (e)What is the outcome and the conclusion of this test?
(a)Use a t-sampling distribution because the population is normal, and σ is unknown. (b)H0:μ≥24 Ha:μ<24 (c)The standardized test statistic is -2.83 use http://www.learningaboutelectronics.com/Articles/Test-statistic-calculator.php#answer (d)The critical value is −1.895. use https://www.omnicalculator.com/statistics/critical-value (e)Reject H0. At the 5% significance level, there is sufficient evidence to reject the carcompany's claim that the mean gas mileage for the luxury sedan is at least 24 miles per gallon.
For the following information, determine whether a normal sampling distribution can be used, where p is the population proportion, α is the level of significance, p is the sample proportion, and n is the sample size. If it can be used, test the claim. Claim: p≥0.25; α=0.04. Sample statistics: p=0.20, n=180 (a)Let q=1−p and let q=1−p. A normal sampling distribution ______ be used here, since ___ ____5 and ___ ____5. (b)If a normal sampling distribution can be used, identify the hypotheses for testing the claim. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (c)If a normal sampling distribution can be used, identify the critical value(s) for this test. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (d)If a normal sampling distribution can be used, identify the rejection region(s). Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. (e)If a normal sampling distribution can be used, identify standardized test statistic z. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (f)If a normal sampling distribution can be used, decide whether to reject or fail to reject the null hypothesis and interpret the decision. Choose the correct answer below.
(a)can, np, ≥, nq, ≥ (b)H0:p≥0.25, Ha: p<0.25 (c) -1.76 use https://www.omnicalculator.com/statistics/critical-value (d)The rejection region is z<−1.75. (e)z=-1.55 use 1 prop z test in calculator, use 25, 36(.20x180), 180, and <p0 (f)Fail to reject the null hypothesis. There is not enough evidence to reject the claim.
For the following information, determine whether a normal sampling distribution can be used, where p is the population proportion, α is the level of significance, p is the sample proportion, and n is the sample size. If it can be used, test the claim. Claim: p>0.45; α=0.06. Sample statistics: p=0.52, n=225 (a)Let q=1−p and let q=1−p. A normal sampling distribution ___ be used here, since ____ ___5 and ___ ____5. (b)If a normal sampling distribution can be used, identify the hypotheses for testing the claim. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. (c)If a normal sampling distribution can be used, identify the critical value(s) for this test. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (d)If a normal sampling distribution can be used, identify the rejection region(s). Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. (e)If a normal sampling distribution can be used, identify standardized test statistic z. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (f)If a normal sampling distribution can be used, decide whether to reject or fail to reject the null hypothesis and interpret the decision. Choose the correct answer below.
(a)can, np, ≥, nq,≥ (b)H0:p≤. 45 Ha:p>. 45 (c)z0=1.55 use https://www.omnicalculator.com/statistics/critical-value (z distribution, right tailed) (d)The rejection region is z>1.56 use https://www.omnicalculator.com/statistics/critical-value (t-student ,right tailed) (e)z=2.11 use 1 prop z test in calculator(use .45, 117(.52x225),225, >p0 (f)Reject the null hypothesis. There is enough evidence to support the claim.
(a)What are the two types of hypotheses used in a hypothesis test? (b)How are they related?
(a)null and alternative (b)They are complements.
Use the given statement to represent a claim. Write its complement and state which is H0 and which is Ha. p>0.61 (a)Find the complement of the claim. (b)Which is H0 and which is Ha?
(a)p≤61 (b)H0:p≤0.61 Ha:p>0.61
Use the given statement to represent a claim. Write its complement and state which is H0 and which is Ha. μ≥371 (a)Find the complement of the claim. (b)Which is H0 and which is Ha?
(a)μ<371 (b)H0:μ≥371 Ha:μ<371
Use the given statement to represent a claim. Write its complement and state which is H0 and which is Ha. σ≠9 (a)Find the complement of the claim. (b)Which is H0 and which is Ha?
(a)σ=9 (b)H0:σ=9 Ha:σ≠9
Decide whether the normal sampling distribution can be used. If it can be used, test the claim about the population proportion p at the given level of significance α using the given sample statistics. Claim: p≠0.27; α=0.01; Sample statistics: p=0.21, n=100 (a)Can the normal sampling distribution be used? (b)State the null and alternative hypotheses. (c)Determine the critical value(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (d)Find the z-test statistic. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (e)What is the result of the test?
(a)Yes, because both np and nq are greater than or equal to 5. (b)H0:p=0.27 Ha:p≠0.27 (c)The critical value(s) is/are 2.58,−2.58 use https://www.omnicalculator.com/statistics/critical-value (two tailed, z distribution) (d)z=-1.35 use 1 prop z test in calculator(use .27, 21(.21x100),100, ≠p0 (e)Fail to reject H0. The data do not provide sufficient evidence to support the claim.
A local chess club claims that the length of time to play a game has a mean of 39 minutes or less. Write sentences describing type I and type II errors for a hypothesis test of this claim.
A type I error will occur if the actual mean of the length of time to play a game is (less than or equal to) 39 minutes, but you (reject) the null hypothesis, Ho: μ≤39. A type II error will occur if the actual mean of the length of time to play a game is (greater than) 39 minutes, but you (fail to reject) the null hypothesis, H0: μ≤39.
What conditions are necessary in order to use the dependent samples t-test for the mean of the difference of two populations?
Each sample must be randomly selected from a normal population and each member of the first sample must be paired with a member of the second sample.
What conditions are necessary in order to use the z-test to test the difference between two population proportions? Choose the correct answer below.
Each sample must be randomly selected, independent, and n1p1, n1q1, n2p2, and n2q2 must be at least five.
What conditions are necessary in order to use the z-test to test the difference between two population proportions?
Each sample must be randomly selected, independent, and n1p1, n1q1, n2p2, and n2q2 must be at least five.
Use the technology display to make a decision to reject or fail to reject the null hypothesis at α=0.05. Make the decision using the standardized test statistic and using the P-value. Assume the sample sizes are equal.
Fail to reject the null hypothesis because the P-value is greater than the level of significance.
In a hypothesis test, you assume the alternative hypothesis is true.
False. In a hypothesis test, you assume the null hypothesis is true.
What conditions are necessary in order to use a t-test to test the differences between two population means?
The population standard deviations are unknown. The samples are randomly selected and independent. The populations are normally distributed or each sample size is at least 30.
Match each P-value with the graph that displays its area without performing any calculations. Explain your reasoning. P=0.0154 and P=0.2676.
Graph (a)displays the area for P=0.0154 and graph (b)displays the area for P=0.2676 because the P-value is equal to the shaded area.
Explain how to decide when a normal distribution can be used to approximate a binomial distribution.
If np≥5 and nq≥5, the normal distribution can be used.
Why is a level of significance of α=0 not used?
If α=0, the null hypothesis cannot be rejected, making the hypothesis test useless.
Explain the difference between the z-test for μ using rejection region(s) and the z-test for μ using a P-value.
In the z-test using rejection region(s), the test statistic is compared with critical values. The z-test using a P-value compares the P-value with the level of significance α.
Explain the difference between the z-test for μ using rejection region(s) and the z-test for μ using a P-value. Choose the correct answer below.
In the z-test using rejection region(s), the test statistic is compared with critical values. The z-test using a P-value compares the P-value with the level of significance α.
In hypothesis testing, does choosing between the critical value method or the P-value method affect your conclusion? Explain.
No, because both involve comparing the test statistic's probability with the level of significance.
In hypothesis testing, does choosing between the critical value method or the P-value method affect your conclusion? Explain. Choose the correct answer below.
No, because both involve comparing the test statistic's probability with the level of significance.
When P>α, does the standardized test statistic lie inside or outside of the rejection region(s)? Explain your reasoning.
Outside; When the standardized test statistic is inside the rejection region, P<α.
What conditions are necessary in order to use a t-test to test the differences between two population means? Choose the correct answer below.
The population standard deviations are unknown. The samples are randomly selected and independent. The populations are normally distributed or each sample size is at least 30.
Use the technology display to make a decision to reject or fail to reject the null hypothesis at α=0.10. Make the decision using the standardized test statistic and using the P-value. Assume the sample sizes are equal.
Reject the null hypothesis because theP-value is less than the level of significance.
Use the calculator displays to the right to make a decision to reject or fail to reject the null hypothesis at a significance level of α=0.05.
Since the P-value is greater than α, fail to reject the null hypothesis.
Explain how to perform a two-sample t-test for the difference between two population means.
State the hypotheses and identify the claim. Specify the level of significance. Determine the degrees of freedom. Find the critical value(s) and identify the rejection region(s). Find the standardized test statistic. Make a decision and interpret it in the context of the original claim.
Explain how to perform a two-sample t-test for the difference between two population means. Which explanation below best describes how to perform the two-sample t-test?
State the hypotheses and identify the claim. Specify the level of significance. Determine the degrees of freedom. Find the critical value(s) and identify the rejection region(s). Find the standardized test statistic. Make a decision and interpret it in the context of the original claim.
Explain how to perform a two-sample z-test for the difference between two population means using independent samples with σ1 and σ2 known.
State the hypotheses and identify the claim. Specify the level of significance. Find the critical value(s) and identify the rejection region(s). Find the standardized test statistic. Make a decision and interpret it in the context of the claim.
Explain how to perform a two-sample z-test for the difference between two population means using independent samples with σ1 and σ2 known.
State the hypotheses and identify the claim. Specify the level of significance. Find the critical value(s) and identify the rejection region(s). Find the standardized test statistic. Make a decision and interpret it in the context of the claim.
Explain how to perform a two-sample z-test for the difference between two population proportions.
State the hypotheses and identify the claim. Specify the level of significance. Find the critical value(s) and rejection region(s). Find p and q. Find the standardized test statistic. Make a decision and interpret it in the context of the claim.
Explain how to perform a two-sample z-test for the difference between two population proportions. Choose the best answer.
State the hypotheses and identify the claim. Specify the level of significance. Find the critical value(s) and rejection region(s). Find p and q. Find the standardized test statistic. Make a decision and interpret it in the context of the claim.
How are null and alternative hypotheses related?
They are complements.
Explain why the null hypothesis H0: μ1=μ2 is equivalent to the null hypothesis H0: μ1−μ2=0.
They are equivalent through algebraic manipulation.
Explain why the null hypothesis H0: μ1≥μ2 is equivalent to the null hypothesis H0: μ1−μ2≥0.
They are equivalent through algebraic manipulation.
Explain why the null hypothesis H0: μ1≥μ2 is equivalent to the null hypothesis H0: μ1−μ2≥0.
They are equivalent through algebraic manipulation.
If you decide to reject the null hypothesis, then you can support the alternative hypothesis.
This statement is true.
A null and alternative hypothesis are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. H0:σ=6.6 Ha:σ≠6.6 What type of test is being conducted in this problem?
Two-tailed test
What are the two types of hypotheses used in a hypothesis test?
null and alternative
What are the two decisions that you can make from performing a hypothesis test?
reject the null hypothesis & fail to reject the null hypothesis
