SOLUTION: Students of the author estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Uses a 0.05 significance level to test t

Question 1204608: Students of the author estimated the length of one minute without reference to a watch or clock, and the times
(seconds) are listed below. Uses a 0.05 significance level to test the claim that these times are from a population with
mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one minute? Assume times
are normally distributed.
69 81 39 65 42 21 60 63 66 48 64 70 96 91 65
a. State the null and alternative hypotheses.
b. Use technology to calculate the test statistic and P - Value. [Put the values in L1 (say). Then go to STAT ----
TESTS ---- T-Test --- Input: select Data, and complete the rest]
c. Use Critical - Value Method to do the test. Find the critical value and use the Test Statistic you calculated from
(b)
d. Use P - Value Method to do the test. The P - Value you calculated from (b).

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
i used a one sample t-test calculator at https://www.statskingdom.com/130MeanT1.html
the sample mean was 62.6667.
the sample standard deviation was 19.4814.
the t-score was equal to .5301 and the p-score was equal to .6043.
sample size was 15; degrees of freedom was 14; critical t-score at 95% confidence interval was t = plus or minus 2.1448; critical p-score was .05 (.025 at each end of the confidence interval).
the test t-score was less than the critical t-score and the test p-score was greater than the critical p-score.
this indicates the reqults were not significant.
the conclusion was that there was not suficient information to say that the number of seconds in a minute was different than the expected value of 60.
i used the ti-84 plus calculator (entered the data in L1 and then did a t-test.
ti-84 commands were:
stat > 1 to get into the list edit mode.
then enter the data in l1.
then quit (2d mode)
then stat > tests > 2 for t-test.
then data for input, 60 for mean, L1 for list (2d 1), 1 for freq, not equal for mu0, then calculate.
that gives the results of the t-test on the data that is stored in L1.
the output of the online calculator is shown below:

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