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 23 24 22 25 28 27 34 32 37 34 Pleasantness Rating 0.1 1.0 1.2 1.2 1.0 2.0 2.3 2.2 2.5 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 to find the critical value. Round your answers to three decimal places.) Interpret the resulting interval. O We are 95% confident that the mean change in firing frequency associated with an increase of 1 in pleasantness rating is in this interval. O We are 95% confident that the mean change in firing frequency associated with an increase of 1 in pleasantness rating is outside this interval. O 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. Ⓒ 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. (b) Carry out a hypothesis test using a = 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.) Use technology to find the P-value for this test. (Round your answer to four decimal places.) P-value= What can you conclude? O Reject H. We do not have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating. O Reject Ho. We have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating. O Fail to reject H. We do not have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating. O Fail to reject Ho. We have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating.
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 23 24 22 25 28 27 34 32 37 34 Pleasantness Rating 0.1 1.0 1.2 1.2 1.0 2.0 2.3 2.2 2.5 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 to find the critical value. Round your answers to three decimal places.) Interpret the resulting interval. O We are 95% confident that the mean change in firing frequency associated with an increase of 1 in pleasantness rating is in this interval. O We are 95% confident that the mean change in firing frequency associated with an increase of 1 in pleasantness rating is outside this interval. O 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. Ⓒ 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. (b) Carry out a hypothesis test using a = 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.) Use technology to find the P-value for this test. (Round your answer to four decimal places.) P-value= What can you conclude? O Reject H. We do not have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating. O Reject Ho. We have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating. O Fail to reject H. We do not have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating. O Fail to reject Ho. We have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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Transcribed Image Text: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
23
24
22
25
28
27
34
32
37
34
Pleasantness Rating
0.1
1.0
1.2
1.2
1.0
2.0
2.3
2.2
2.5
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 to find the critical value. Round your answers to three decimal places.)
Interpret the resulting interval.
O 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 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.
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.
(b) Carry out a hypothesis test using a = 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?
O Reject H. We do not have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating.
O Reject Ho. We have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating.
O Fail to reject Ho. We do not have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating.
O Fail to reject Ho. We have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating.
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