A coin was tossed 100 times. The result was 58 times showing heads and 42 times showing tails. Test the hypothesis that the coin is symmetrical using a significance level of α = 0.05!
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A coin was tossed 100 times. The result was 58 times showing heads and 42 times showing tails. Test the hypothesis that the coin is symmetrical using a significance level of α = 0.05!
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- The manufacturer of a new eye cream claims that the cream reduces the appearance of fine lines and wrinkles after just 14 days of application. To test the claim, 10 women are randomly selected to participate in a study. The number of fine lines and wrinkles that are visible around each participant’s eyes is recorded before and after the 14 days of treatment. The following table displays the results. Test the claim at the 0.05 level of significance assuming that the population distribution of the paired differences is approximately normal. Let women before the treatment be Population 1 and let women after the treatment be Population 2. Number of Fine Lines and WrinklesBefore 11 14 13 12 15 14 9 11 11 14After 10 14 11 13 13 13 8 12 10 15 Step 1 of 3 : State the n ull and alternative hypotheses for the test. Fill in the blank below. H0Ha: μd=0: μd⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯0 3) draw a conclusion and form a decision (word it like "we…A major oil company has developed a new gasoline additive that is supposed to increase mileage. To test this hypothesis, ten cars are randomly selected. The cars are driven both with and without the additive. The results are displayed in the following table. Can it be concluded, from the data, that the gasoline additive does significantly increase mileage? Let d= (gas mileage with additive)-(gas mileage without additive). Use a significance level of a = 0.01 for the test. Assume that the gas mileages are normally distributed for the population of all cars both with and without the additive. Car 1 Without additive 17.7 With additive 2 3 5 7 11.1 27.2 18.7 20.2 26.2 19.8 20 14.2 28.3 21.1 21.7 27.5 20.5 Step 1 of 5: State the null and alternative hypotheses for the test. 4 6 8 26 28.2 9 9.6 23.5 12.8 24.9 10 Copy DataThe manufacturer of a new eye cream claims that the cream reduces the appearance of fine lines and wrinkles after just 14 days of application. To test the claim, 10 women are randomly selected to participate in a study. The number of fine lines and wrinkles that are visible around each participant's eyes is recorded before and after the 14 days of treatment. The following table displays the results. Test the claim at the 0.02 level of significance assuming that the population distribution of the paired differences is approximately normal. Let women before the treatment be Population 1 and let women after the treatment be Population 2. Number of Fine Lines and Wrinkles Before 12 14 13 11 11 15 10 10 10 9 After 10 14 12 12 12 15 9 7 8 Copy Data Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places.
- According to a certain government agency for a large country, the proportion of fatal traffic accidents in the country in which the driver had a positive blood alcohol concentration (BAC) is 0.34. Suppose a random sample of 113 traffic fatalities in a certain region results in 52 that involved a positive BAC. Does the sample evidence suggest that the region has a higher proportion of traffic fatalities involving a positive BAC than the country at the x = 0.05 level of significance? Because npo (1 - Po) = 25.4 > 10, the sample size is sample is given to be random, satisfied. (Round to one decimal place as needed.) What are the null and alternative hypotheses? less than 5% of the population size, and the the requirements for testing the hypothesis are Ho: P = 0.34 versus H₁: p > 0.34 (Type integers or decimals. Do not round.) Find the test statistic, Zo Zo = (Round to two decimal places as needed.)According to a certain government agency for a large country, the proportion of fatal traffic accidents in the country in which the driver had a positive blood alcohol concentration (BAC) is 0.32. Suppose a random sample of 108 traffic fatalities in a certain region results in 45 that involved a positive BAC. Does the sample evidence suggest that the region has a higher proportion of traffic fatalities involving a positive BAC than the country at the a = 0.05 level of significance? Because npo (1- Po) 10, the sample size is 5% of the population size, and the sample | the requirements for testing the hypothesis satisfied. (Round to one decimal place as needed.)Researchers conducted trials to investigate the effects of color on creativity. Subjects with a red background were asked to think of creative uses for a brick; other subjects with a blue background were given the same task. Responses were scored by a panel of judges and results from scores of creativity are given in the accompanying table. Higher scores correspond to more creativity. The researchers make the claim that "blue enhances performance on a creative task." Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b). Click the icon to view the summary statistics. a. Use a 0.01 significance level to test the claim that blue enhances performance on a creative task. What are the null and alternative hypotheses? OA. Ho: H₁ H₂ H₁: H₁ H₂ OC. Ho: H₁ H₂ H₁: H₁ H₂ The test statistic, t, is (Round to two decimal places as needed.) The…
- A random sample of 54 students from a college are selected from a normal population with mu equal to 20 and sigma equal to 5. After a treatment is administered to the students, the researcher calculated the sample mean to be 21. Is there enough evidence to conclude that the treatment had a significant effect at the 5% significance level? How many tails does this test have?An accountant is studying how much American families donate each year to charity. The accountant states the average yearly amount donated to charity by American families is different than 5.5 thousand dollars. If we would like to test the accountant's claim with a hypothesis test using a significance level of α=0.01 , what is the rejection region? Use the graph below to show the rejection region. First, move the blue dot to choose the appropriate test (left-, right, or two- tailed). Then, slide the shaded region(s) to represent the rejection region.According to a certain government agency for a large country, the proportion of fatal traffic accidents in the country in which the driver had a positive blood alcohol concentration (BAC) is 0.38. Suppose a random sample of 105 traffic fatalities in a certain region results in 51 that involved a positive BAC. Does the sample evidence suggest that the region has a higher proportion of traffic fatalities involving a positive BAC than the country at the a = 0.01 level of significance? Because npo (1 - Po 10, the sample size is 5% of the population size, and the sample the requirements for testing the hypothesis satisfied. (Round to one decimal place as needed.) can be reasonably assumed to be random, What are the null and alternative hypotheses? is given to be random, cannot be reasonably assumed to be random, Ho: versus H,: (Type integers or decimals. Do not round.) is given to not be random, Find the test statistic, zo. Z0 = (Round to two decimal places as needed.) Find the P-value.…
- collected data from 150 surveys ne nanaed out at a busy park located in the region. To continue the study into the drinking habits of adults, the researcher decides to collect data from adults working in "white collar" jobs to see whether their drinking habits are in the same proportion as the general public. The null hypothesis for this test is Ho: p = 0.26 and the alternative hypothesis is Ha: p<0.26. The researcher collected data from a random sample of 120 adults with "white collar" jobs of which 25 stated that they drank once a week or less in the last month. Assume that the conditions that must be met in order for us to use the N(0, 1) distribution as the sampling distribution are satisfied. Find the values of the sample proportion, p, the test statistic, and the p-value associated with the test statistic. Round all values to the nearest thousandth. P = 0.30, z = 0.803, p-value = 0.041 A P = 0.208, z = -1.290, p-value = 0.098 P = 0.75, z = -1.32, p-value = 0.599 P = 0.208, z =…ester Hollar is vice president for human resources for a large manufacturing company. In recent years, he has noticed an increase in absenteeism that he thinks is related to the general health of the employees. Four years ago, in an attempt to improve the situation, he began a fitness program in which employees exercise during their lunch hour. To evaluate the program, he selected a random sample of eight participants and found the number of days each was absent in the six months before the exercise program began and in the six months following the exercise program. Below are the results. Employee Before After 1 6 5 2 6 2 3 7 1 4 7 3 5 4 3 6 3 6 7 5 3 8 6 7 At the 0.05 significance level, can he conclude that the number of absences has declined? Estimate the p-value. State the decision rule for 0.05 significance level. (Round your answer to 3 decimal places.) Compute the test statistic. (Round your answer to 3 decimal places.)According to a certain government agency for a large country, the proportion of fatal traffic accidents in the country in which the driver had a positive blood alcohol concentration (BAC) is 0.34. Suppose a random sample of 109 traffic fatalities in a certain region results in 50 that involved a positive BAC. Does the sample evidence suggest that the region has a higher proportion of traffic fatalities involving a positive BAC than the country at the x = 0.01 level of significance? Because npo (1-Po) = 24.5 > 10, the sample size is (Round to one decimal place as needed.) What are the null and alternative hypotheses? p = 0.34 versus H₁: p > 0.34 Ho: p (Type integers or decimals. Do not round.) Find the test statistic, Zo. Zo = 2.62 (Round to two decimal places as needed.) Find the P-value. P-value = (Round to three decimal places as needed.) less than 5% of the population size, and the sample is given to be random, the requirements for testing the hypothesis are satisfied.
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