Test the claim that the treatment population and the placebo population have different variances at a significance level of α = 0.05. Assume that the populations are normally distributed. n x s Treatment 8 23.55 0.52 Placebo 16 26.81 0.59 Is there sufficient evidence to reject the null hypothesis? A. Yes, because the test statistic fell in the critical region. B. Yes, because the test statistic did not fall in the critical region. C. No, because the test statistic fell in the critical region. D. No, because the test statistic did not fall in the critical region.
A study was conducted to determine whether magnets were effective in treating pain. The values represent pain measurements. Use a 0.05 significance level to test the claim that those given a sham treatment have greater variation in pain reductions than those treated with magnets. Assume that the populations are normally distributed. n x s Magnet 31 0.46 0.78 Sham 21 0.46 1.43 Is there sufficient evidence to reject the null hypothesis? A. No, because the test statistic did not fall in the critical region. B. Yes, because the test statistic did not fall in the critical region. C. No, because the test statistic fell in the critical region. D. Yes, because the test statistic fell in the critical region.
When 14 different second-year medical students measured the systolic blood pressure of the same person, they obtained the results listed below (in mmHg). Assuming that the population standard deviation is known to be 10mmHg, use a 0.05 significance level to test the claim that the mean blood pressure level is less than 140mmHg. Hypertension is defined to be a blood pressure level that is too high because it is 140mmHg or greater. Assume the blood pressure levels are normally distributed. Based on the hypothesis test results, can it be safely concluded that the person does not have hypertension? Click here to view page 1 of the standard normal table. 1 Click here to view page 2 of the standard normal table. 2 (a) Identify the null hypothesis and alternative hypothesis. A. H0 : µ = 140 versus H1 : µ 6= 140 B. H0 : µ = 140 versus H1 : µ > 140 C. H0 : µ = 140 versus H1 : µ < 140 (b) Identify the test statistic. z = (Round the final answer to two decimal places as needed. Round all intermediate values to two decimal places.) (c) Identify the P-value. The P-value is. (Round to three decimal places as needed.) (d) What is the final conclusion? A. Fail to reject H0. There is sufficient evidence to support the claim. B. Reject H0. There is not sufficient evidence to support the claim. C. Reject H0. There is sufficient evidence to support the claim. D. Fail to reject H0. There is not sufficient evidence to support the claim. (e) Can it be safely concluded that the person does not have hypertension? Yes No
Test the following claim. Identify the null hypothesis, alternative hypothesis, test statistic, critical value(s), conclusion about the null hypothesis, and final conclusion that addresses the original claim. Tests of older baseballs showed that when dropped 22ft onto a concrete surface, they bounced an average of 237.1 cm. In a test of 50 new baseballs, the bounce heights had a mean of 239.1 cm. Assume that the standard deviation of bounce heights of all new baseballs is 4.2 cm. Use a 0.01 significance level to test the claim that the new baseballs have bounce heights with a mean different from 237.1 cm. Are the new baseballs different? What are the null and alternative hypotheses? A. H0 : µ ≤ 237.1 cm H1 : µ > 237.1 cm C. H0 : µ = 237.1 cm H1 : µ = 237.1 cm B. H0 : µ = 237.1 cm H1 : µ 6= 237.1 cm D. H0 : µ ≥ 237.1 cm H1 : µ < 237.1 cm What is the value of the test statistic? z = (Round to two decimal places as needed.) Identify the critical value(s) of z. z = (Round to two decimal places as needed. Use a comma to separate answers as needed.) (1) H0. There (2) sufficient evidence to support the claim that the new baseballs are different. (1) Reject (2) is Fail to reject is not
Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. In a manual on how to have a number one song, it is stated that a song must be no longer than 210 seconds. A simple random sample of 40 current hit songs results in a mean length of 236.8sec and a standard deviation of 56.81sec. Use a 0.05 significance level and the accompanying Minitab display to test the claim that the sample is from a population of songs with a mean greater than 210sec. What do these results suggest about the advice given in the manual? 3 Click the icon to view the Minitab display. What are the hypotheses? A. H0 : µ = 210sec H1 : µ ≤ 210sec C. H0 : µ = 210sec H1 : µ > 210sec B. H0 : µ < 210sec H1 : µ > 210sec D. H0 : µ > 210sec H1 : µ ≤ 210sec Identify the test statistic. t = (Round to two decimal places as needed.) Identify the P-value. The P-value is (Round to three decimal places as needed.) State the final conclusion that addresses the original claim. Choose the correct answer below. A. Fail to reject H0. There is insufficient evidence to support the claim that the sample is from a population of songs with a mean length greater than 210sec. B. Fail to reject H0. There is sufficient evidence to support the claim that the sample is from a population of songs with a mean length greater than 210sec. C. Reject H0. There is insufficient evidence to support the claim that the sample is from a population of songs with a mean length greater than 210sec. D. Reject H0. There is sufficient evidence to support the claim that the sample is from a population of songs with a mean length greater than 210sec. What do the results suggest about the advice given in the manual? A. The results suggest that 236.8 seconds is the best song length. B. The results suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice. C. The results do not suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice. D. The results are inconclusive because the average length of a hit song is constantly changing. 3: Minitab display One-Sample T Test of mu = 210 vs > 210 N Mean StDev SE Mean Bound T P 40 236.80 56.81 8.98 221.67 2.98 0.002
751 body temperature measurements were taken. The sample data resulted in a sample mean of 98.3◦F and a sample standard deviation of 0.7◦F. Use the traditional method and a 0.05 significance level to test the claim that the mean body temperature is less than 98.6◦F. 4 Click the icon to view a table of critical t-values. Choose the correct answer below. A. Do not reject H0 since the test statistic -0.085 is not less than the critical value -1.647. B. Reject H0 since the test statistic -11.745 is less than the critical value -1.647. C. Reject H0 since the test statistic is -0.085 not less than the critical value -1.647. D. Do not reject H0 since the test statistic -11.745 is less than the critical value -1.647.
Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. A safety administration conducted crash tests of child booster seats for cars. Listed below are results from those tests, with the measurements given in hic (standard head injury condition units). The safety requirement is that the hic measurement should be less than 1000 hic. Use a 0.01 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified requirement? 808 742 1306 629 650 545 What are the hypotheses? A. H0 : µ > 1000 hic H1 : µ < 1000 hic C. H0 : µ = 1000 hic H1 : µ ≥ 1000 hic B. H0 : µ = 1000 hic H1 : µ < 1000 hic D. H0 : µ < 1000 hic H1 : µ ≥ 1000 hic Identify the test statistic. t = (Round to three decimal places as needed.) Identify the P-value. The P-value is (Round to four decimal places as needed.) State the final conclusion that addresses the original claim. (1) H0. There is (2) evidence to support the claim that the sample is from a population with a mean less than 1000 hic. What do the results suggest about the child booster seats meeting the specified requirement? A. There is not strong evidence that the mean is less than 1000 hic, and one of the booster seats has a measurement that is greater than 1000 hic. B. The results are inconclusive regarding whether one of the booster seats could have a measurement that is greater than 1000 hic. C. There is strong evidence that the mean is less than 1000 hic, but one of the booster seats has a measurement that is greater than 1000 hic. D. The requirement is met since most sample measurements are less than 1000 hic. (1) Reject (2) insufficient Fail to reject sufficient
Calculate the test statistic, find the critical value(s) of χ2 , and use a χ2 distribution table to find the limits containing the P-value. Determine whether there is sufficient evidence to support the given alternative hypothesis. Test H0 : σ = 3.39 versus H1 : σ 6= 3.39, given that α = 0.10, n = 16, and s = 3.55. Compute the test statistic. χ2 = (Round to three decimal places as needed.) Find the critical value(s). (Use a comma to separate answers as needed. Round to three decimal places as needed.) Find the limits that contain the P-value. A. 0.1 < P-value < 0.2 B. 0.01 < P-value < 0.02 C. 0.05 < P-value < 0.1 D. 0.2 < P-value < 1 Is there sufficient evidence to support the alternative hypothesis? A. Yes, because the test statistic is within the critical region and the P-value is less than or equal to the level of significance. B. Yes, because the test statistic is outside the critical region and the P-value is greater than the level of significance. C. No, because the test statistic is within the critical region and the P-value is less than or equal to the level of significance. D. No, because the test statistic is outside the critical region and the P-value is greater than the level of significance.
Calculate the test statistic, find the critical value(s) of χ2, and use a χ2 distribution table to find the limits containing the P-value. Determine whether there is sufficient evidence to support the given alternative hypothesis. Test H0 : σ = 14 versus H1 : σ < 14, given that α = 0.025, n = 20, and s = 10. Compute the test statistic. χ2 = (Round to three decimal places as needed.) Find the critical value(s). (Use a comma to separate answers as needed. Round to three decimal places as needed.) Find the limits containing the P-value. A. 0.975 < P-value < 0.99 B. 0.025 < P-value < 0.05 C. 0.99 < P-value < 0.995 D. 0.1 < P-value < 0.9 Is there sufficient evidence to support the alternative hypothesis? A. No, because the test statistic is within the critical region and the P-value is less than or equal to the level of significance. B. No, because the test statistic is outside the critical region and the P-value is greater than the level of significance. C. Yes, because the test statistic is outside the critical region and the P-value is greater than the level of significance. D. Yes, because the test statistic is within the critical region and the P-value is less than or equal to the level of significance.
Use a 0.05 significance level to test the claim that peanut candies have weights that vary more than plain candies. The standard deviation for the weights of plain candies is 0.095. A sample of 61 peanut candies has weights with a standard deviation of 0.28. Do peanut candies have weights that vary more than those of plain candies? A. Since H0 : σ > 0.095 is not rejected, the weights do not vary more for peanut candies. B. Since H0 : σ = 0.095 is rejected, the weights vary more for peanut candies. C. Since H0 : σ = 0.095 is not rejected, the weights do not vary more for peanut candies. D. Since H0 : σ > 0.095 is rejected, the weights vary more for peanut candies.