Researchers studying pleasant touch sensations measured the firing frequency (impulses per second) of nerves that were stimulated by a light brushing stroke on the forearm and also recorded the subject's numerical rating of how pleasant the sensation was. The accompanying data was read from a graph in a paper. Firing Frequency Pleasantness Rating 23 0.1 24 1.0 22 1.2 25 1.2 28 1.0 27 2.0 34 2.3 34 2.2 37 2.5 34 2.7 (a) Estimate the mean change in pleasantness rating associated with an increase of 1 impulse per second in firing frequency using a 95% confidence interval. (Use technology or the Distribution Calculators page in SALT to find the critical value. Round your answers to three decimal places.) ( , ) Interpret the resulting interval. We are 95% confident that the mean change in firing frequency associated with an increase of 1 in pleasantness rating is in this interval. We are 95% confident that the mean change in pleasantness rating associated with an increase of 1 impulse per second in firing frequency is outside this interval. We are 95% confident that the mean change in firing frequency associated with an increase of 1 in pleasantness rating is outside this interval. We are 95% confident that the mean change in pleasantness rating associated with an increase of 1 impulse per second in firing frequency is in this interval. (b) Carry out a hypothesis test using ? = 0.05 to decide if there is convincing evidence of a useful linear relationship between firing frequency and pleasantness rating. Calculate the test statistic. (Round your answer to two decimal places.) t = Use technology to find the P-value for this test. (Round your answer to four decimal places.) P-value = What can you conclude? Reject H0. We do not have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating. Reject H0. We have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating. Fail to reject H0. We do not have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating. Fail to reject H0. We have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating.
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Given: - Differences in pleasantness rating: 0.1, 1.0, 1.2, 1.2, 1.0, 2.0, 2.3, 2.2, 2.5, 2.7 Mean difference = (0.1 + 1.0 + 1.2 + 1.2 + 1.0 + 2.0 + 2.3 + 2.2 + 2.5 + 2.7) / 10 Mean difference = 1.42 / 10 Mean difference = 0.142 Show more…
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Researchers studying pleasant touch sensations measured the firing frequency (impulses per second) of nerves that were stimulated by a light brushing stroke on the forearm and also recorded the subject's numerical rating of how pleasant the sensation was. The accompanying data was read from a graph in a paper. Firing Frequency Pleasantness Rating 23 0.1 24 1.0 22 1.2 25 1.2 28 1.0 27 2.0 34 2.3 34 2.2 37 2.5 34 2.7 (a) Estimate the mean change in pleasantness rating associated with an increase of 1 impulse per second in firing frequency using a 95% confidence interval. (Use technology or the Distribution Calculators page in SALT to find the critical value. Round your answers to three decimal places.) ( , ) Interpret the resulting interval. We are 95% confident that the mean change in firing frequency associated with an increase of 1 in pleasantness rating is in this interval. We are 95% confident that the mean change in pleasantness rating associated with an increase of 1 impulse per second in firing frequency is outside this interval. We are 95% confident that the mean change in firing frequency associated with an increase of 1 in pleasantness rating is outside this interval. We are 95% confident that the mean change in pleasantness rating associated with an increase of 1 impulse per second in firing frequency is in this interval. (b) Carry out a hypothesis test using ̑ = 0.05 to decide if there is convincing evidence of a useful linear relationship between firing frequency and pleasantness rating. Calculate the test statistic. (Round your answer to two decimal places.) t = Use technology to find the P-value for this test. (Round your answer to four decimal places.) P-value = What can you conclude? Reject H₀. We do not have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating. Reject H₀. We have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating. Fail to reject H₀. We do not have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating. Fail to reject H₀. We have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating.
Madhur L.
Firing Frequency Pleasantness Rating 23 0.1 24 1.0 22 1.2 25 1.2 28 1.0 27 2.0 34 2.3 34 2.2 37 2.5 34 2.7 Estimate the mean change in pleasantness rating associated with an increase of 1 impulse per second in firing frequency using a 95% confidence interval. Interpret the resulting interval. We are 95% confident that the mean change in pleasantness rating associated with an increase of 1 impulse per second in firing frequency is in this interval. Calculate the test statistic. (Round your answer to two decimal places.) Use technology to find the P-value for this test. (Round your answer to four decimal places.) Reject H0. We have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating. Fail to reject H0. We do not have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating.
The burning rates of two different solid-fuel propellants used in aircrew escape systems are being studied. It is known that both propellants have approximately the same standard deviation of burning. Random samples of the propellants are tested, and the sample mean burning rates are measured. The first sample mean burning rate is denoted as X1, and the second sample mean burning rate is denoted as X2. (a) Test the hypothesis that both propellants have the same mean burning rate. Use a significance level of 0.05. What is the p-value? (b) Construct a 95% confidence interval on the difference in means, denoted as L1 - L2. (c) What is the error of the test in part (a) if the true difference in mean burning rates is 2.5 centimeters per second? (d) Assuming equal sample sizes, what sample size is needed to obtain a power of 0.9 at a difference in means of 2.5 cm/s? (a) The null hypothesis is rejected. The p-value is [Round your answer to two decimal places]. (b) The 95% confidence interval is [Round your answer to two decimal places]. (c) The error of the test in part (a) is [Round your answer to five decimal places]. (d) The required sample size is [Round your answer to the next integer].
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