Concept explainers
You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001.
Ho:p1=p2Ho:p1=p2
Ha:p1<p2Ha:p1<p2
You obtain 47 successes in a sample of size n1=208n1=208 from the first population. You obtain 182 successes in a sample of size n2=532n2=532 from the second population. For this test, you should NOT use the continuity correction, and you should use the
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =
The p-value is...
- less than (or equal to) αα
- greater than αα
This test statistic leads to a decision to...
- reject the null
- accept the null
- fail to reject the null
As such, the final conclusion is that...
- There is sufficient evidence to warrant rejection of the claim that the first population proportion is less than the second population proportion.
- There is not sufficient evidence to warrant rejection of the claim that the first population proportion is less than the second population proportion.
- The sample data support the claim that the first population proportion is less than the second population proportion.
- There is not sufficient sample evidence to support the claim that the first population proportion is less than the second population proportion.
According to the provided data,
The null and alternative hypotheses are;
This is a lower-tailed test.
The level of significance, α = 0.001.
The sample proportions and pooled proportion is as:
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- ou wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10. Ho:p1=p2Ho:p1=p2 Ha:p1<p2Ha:p1<p2You obtain 84.2% successes in a sample of size n1=746n1=746 from the first population. You obtain 92.4% successes in a sample of size n2=490n2=490 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value =arrow_forwardYou are conducting a study to see if the proportion of voters who prefer Candidate A is significantly different from 61% at a significance level of αα = 0.025. According to your sample, 32 out of 54 potential voters prefer Candidate A. For this study, we should use Select an answer 2-SampTTest 2-PropZInt χ²GOF-Test 1-PropZTest T-Test 2-SampTInt 2-PropZTest χ²-Test 1-PropZInt ANOVA TInterval The null and alternative hypotheses would be: H0H0: ? p μ Select an answer > < = ≠ (please enter a decimal) H1H1: ? μ p Select an answer < > = ≠ (Please enter a decimal) The test statistic = (please show your answer to 3 decimal places.) The p-value = (Please show your answer to 4 decimal places.) The p-value is Select an answer less than (or equal to) greater than αα Based on this, we should Select an answer accept reject fail to reject the null hypothesis. As such, the final conclusion is that ... The sample data suggest tarrow_forward9. A random sample of 135 people yielded the following contingency table describing the relationship between migraine headaches and caffeine consumption (low, medium, high). Caffeine Consumption Low Med. High Migraine 5 8 15 No Migraine 35 42 30 Suppose we wish to test H0 : caffeine and migraines are independent versus Ha : caffeine and migraines are not independent at the α = 0.05 significance level. What is the value of the test statistic and p−value? 10. In reference to question (9), which of the following is/are true? (A) There is not a significant association between caffeine and migraines (B) The test statistic does not fall in the rejection region (C) The critical value is equal to 7.38 D) The expected counts eij are computed assuming caffeine and migraines are independentarrow_forward
- You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly more than 0.16. You use a significance level of α=0.005α=0.005. H0:p=0.16H0:p=0.16 H1:p>0.16H1:p>0.16You obtain a sample of size n=598n=598 in which there are 111 successes.What is the test statistic for this sample? (Report answer accurate to three decimal places.) test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value =arrow_forwardYou are conducting a study to see if the probability of a true negative on a test for a certain cancer is significantly more than 0.14. You use a significance level of α=0.001α=0.001. H0:p=0.14H0:p=0.14 H1:p>0.14H1:p>0.14You obtain a sample of size n=304n=304 in which there are 53 successes.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the probability of a true negative on a test for a certain cancer is more than 0.14. There is not sufficient evidence to warrant rejection of the claim that the probability of a true negative on a test for…arrow_forward10 .You wish to test the following claim (HaHa) at a significance level of α=0.005α=0.005. Ho:p1=p2Ho:p1=p2 Ha:p1≠p2Ha:p1≠p2You obtain a sample from the first population with 97 successes and 375 failures. You obtain a sample from the second population with 76 successes and 189 failures. test statistic = [three decimal accuracy] p-value = [four decimal accuracy] The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null hypothesis fail to reject the null hypothesis As such, the final conclusion is that... There is sufficient evidence to support that the first population proportion is not equal to the second population proportion. There is not sufficient evidence to support that the first population proportion is not equal to the second population proportion.arrow_forward
- You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001. Ho:p1=p2 Ha:p1≠p2You obtain 94% successes in a sample of size n1=796n1=796 from the first population. You obtain 97.9% successes in a sample of size n2=329n2=329 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null hypothesis accept the null hypothesis fail to reject the null hypothesis As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the first population proportion is not…arrow_forwardn a certain school district, it was observed that 30% of the students in the element schools were classified as only children (no siblings). However, in the special program for talented and gifted children, 147 out of 422 students are only children. The school district administrators want to know if the proportion of only children in the special program is significantly different from the proportion for the school district. Test at the α=0.05α=0.05 level of significance.What is the hypothesized population proportion for this test? p=p= (Report answer as a decimal accurate to 2 decimal places. Do not report using the percent symbol.)Based on the statement of this problem, how many tails would this hypothesis test have? one-tailed test two-tailed test Choose the correct pair of hypotheses for this situation: (A) (B) (C) H0:p=0.3Ha:p<0.3 H0:p=0.3Ha:p≠0.3 H0:p=0.3Ha:p>0.3 (D) (E) (F) H0:p=0.348Ha:p<0.348 H0:p=0.348Ha:p≠0.348 H0:p=0.348Ha:p>0.348 (A) (B)…arrow_forwardYou wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10. Ho:p1≥p2Ho:p1≥p2 Ha:p1<p2Ha:p1<p2You obtain a sample from the first population with 240 successes and 413 failures. You obtain a sample from the second population with 321 successes and 390 failures. critical value = [three decimal accuracy] test statistic = [three decimal accuracy] The test statistic is... in the critical region not in the critical region This test statistic leads to a decision to... reject the null hypothesis fail to reject the null hypothesis As such, the final conclusion is that... There is sufficient evidence to support that the first population proportion is less than the second population proportion. There is not sufficient evidence to support that the first population proportion is less than the second population proportion.arrow_forward
- The numbers of online applications from simple random samples of college applications for 2004 and for the 2009 were taken. In 2004, out of 491 applications, 206 of them were completed online. In 2009, out of 268 applications, 145 of them were completed online. Test the claim that the proportion of online applications in 2004 was equal to the proportion of online applications in 2009 at the .10 significance level.Claim: Select an answer p 1 > p 2 u 1≠u 2 p 1≠p 2 u 1 < u 2 p 1 ≥ p 2 u 1 = u 2 p 1 = p 2 u 1 ≥ u 2 p 1 < p 2 p 1 ≤ p 2 u 1 > u 2 u 1 ≤ u 2 which corresponds to Select an answer H1: u 1 < u 2 H0: p 1 ≤ p 2 H1: p 1 > p 2 H0: p 1≠p 2 H1: p 1 < p 2 H1: u 1 > u 2 H1: p 1≠p 2 H1: u 1≠u 2 H0: p 1 = p 2 H0: u 1 ≤ u 2 Opposite: Select an answer u 1 < u 2 u 1 ≤ u 2 p 1 ≥ p 2 p 1 ≤ p 2 p 1 > p 2 p 1 < p 2 u 1 ≠ u 2 p 1 = p 2 u 1 < u 2 u 1 = u 2 u 1 > u 2 p 1≠p 2 which corresponds to Select an answer H1: p 1≠p…arrow_forwardYou are conducting a study to see if the probability of catching the flu this year is significantly less than 0.22. You use a significance level of α=0.005α=0.005. H0:p=0.22H0:p=0.22 H1:p<0.22H1:p<0.22You obtain a sample of size n=430n=430 in which there are 77 successes.What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) αα greater than αα This p-value leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the probability of catching the flu this year is less than 0.22. There is not sufficient evidence to warrant rejection of the claim that the probability of catching the flu this year is less than 0.22. The sample data support the claim that the probability of catching the flu this year is less than 0.22. There is not sufficient sample…arrow_forwardA researcher reports t(22) = 5.30, p < .01 for an independent-measures experiment. How many individuals participated in the entire experiment? Question 15 options: 20 21 23 24arrow_forward
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