Researchers studying pleasant touch sensations measured the firing frequency (impulses per second) of nerves that were stimulated by a ligh brushing stroke on the forearm and also recorded the subject's numerical rating of how pleasant the sensation was. The accompanying data w read from a graph in a paper. Firing Frequency 23 24 22 25 26 29 Pleasantness Rating 0.1 1.0 1.2 1.2 1.0 2.0

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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
23
24
22
25
t =
26
29
34
34
35
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 pleasantness rating associated with an increase of 1 impulse per second in firing
frequency 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.
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 firing frequency associated with an increase of 1 in pleasantness rating is in 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?
Fail to reject Ho. 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 have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating.
O Reject Ho. We do not have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating.
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 t = 26 29 34 34 35 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 pleasantness rating associated with an increase of 1 impulse per second in firing frequency 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. 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 firing frequency associated with an increase of 1 in pleasantness rating is in 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? Fail to reject Ho. 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 have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating. O Reject Ho. We do not have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating.
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