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 thesubject's numerical rating of how pleasant the sensation was. The accompanying data was read from a graph in a paper.Firing Frequency Pleasantness Rating232422252829343437340.31.01.21.21.02.02.32.22.32.9(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 DistributionCalculators page in SALT 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 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 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.)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 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 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.

a) The mean change in pleasantness rating associated with an increase of 1 impulse per second in firing frequency using a 95% confidence interval: Excel Procedure: Enter Firing frequency and Pleasantness Rating in Excel Go to Data Click on Data Analysis> ‘Regression’. Select Pleasantness Rating under ‘Input Y Range’. Select Firing frequency under ‘Input X Range’. Click on ‘OK’. Output: From the output, the 95% confidence interval for the coefficient of firing frequency is (0.069, 0.190) rounded to 3 decimals. Thus, the mean change in pleasantness rating associated with an increase of 1 impulse per second in firing frequency using a 95% confidence interval is (0.069, 0.190). Interpretation: There is a 95% chance that the the mean change in pleasantness rating is lies between the values 0.069 and 0.190. Correct option: We are 95% confidence that the mean change in pleasantness rating associated with an increase of 1 impulse per second in firing frequency is in the interval. b) Null Hypothesis: H0: There is no significant linear relationship between firing frequency and pleasantness rating. Alternative Hypothesis: H1: There is a significant linear relationship between firing frequency and pleasantness rating. Test statistic: From the excel output, the t statistic value corresponding with firing frequency is 4.95. Thus, t=4.95. P value: From the Excel output, the P value corresponding with firing frequency is 0.0011. P value=0.0011. Decision Rule: If p-value ≤ α, then reject the null hypothesis. If p-value > α, then do not reject the null hypothesis. Conclusion: From the given information, the level of significance is α=0.05 The P-value is 0.0011. Here, the P-value is less than the level of significance. From the rejection rule, reject the null hypothesis. There is a significant linear relationship between firing frequency and pleasantness rating. Correct option: Reject H0. We have convincing evidence of a useful linear relationship between firing frequency and pleasantness rating.