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The University is conducting a similar analysis on how much of the 80-minute TR class sessions are used for instruction. There is evidence from a previous study that the population standard deviation for duration time is
2.1
minutes. A random selection of 83 class sessions this semester yields an average duration time of 78 minutes. (a) Calculate a
90%
confidence interval the parameter of interest. (No interpretation needed in your final answer; just the numeric interval.) (a) [5 pts] (b) What is the minimum sample size required to estimate the mean duration time of TR classes to within
0.5
of a minute with
99%
confidence? (b) [5 pts] (c) Suppose that the sample standard deviation for duration times in this study is
2.6
minutes. Calculate a
95%
confidence interval for
σ 2
, the population variance.



Answer :

varshamittal029

The minimum sample size required to estimate the mean duration time of TR classes is t distribution confidence interval.

The confidence interval is 75.0694 and 76.9306.

Given that

(a) This is t-distribution confidence interval because sample standard deviation is given and also sample size is less than 30.

(b)

CI for 95%

n 28

mean 76

value of 95% CI and df = 27 (using  table) 2.0518

std. dev. 2.4

SE = standard deviation/n² 0.45356

ME = t*SE 0.93062

Lower Limit = Mean - ME 75.06938

Upper Limit = Mean + ME 76.93062

95% CI (75.0694 , 76.9306 )

95% CI=75.0694 , 76.9306

(c)The 95% confidence interval estimate of the population mean is within 75.0694 and 76.9306 (lower bound and upper bound)

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