A statistics professor for STAT 250 wants to investigate how long it takes students to complete exercise . The time is recorded in minutes. A student who completed the exercise in 50:30 (50 minutes and 30 seconds) would be recorded as 50.5 minutes a) Summary statistics: Column Mean Std. dev. Time 47.20 8.66 Are these measures you obtained parameters or statistics in part (a) and why? Answer this question in one sentence? Does your confidence interval capture the mean time calculated in part (a)? Answer this question in one sentence. If we were to take 500 samples of size 26 from this population and construct a confidence interval for each sample, approximately how many of these confidence intervals would be expected to capture the mean time calculated in part (a)? Answer this question and provide your reasoning in one or two sentences.
A statistics professor for STAT 250 wants to investigate how long it takes students to complete exercise . The time is recorded in minutes. A student who completed the exercise in 50:30 (50 minutes and 30 seconds) would be recorded as 50.5 minutes
a) Summary statistics:
|
Column |
|
Std. dev. |
|
Time |
47.20 |
8.66 |
Are these measures you obtained parameters or statistics in part (a) and why? Answer this question in one sentence?
Does your confidence interval capture the mean time calculated in part (a)? Answer this question in one sentence.
If we were to take 500 samples of size 26 from this population and construct a confidence interval for each sample, approximately how many of these confidence intervals would be expected to capture the mean time calculated in part (a)? Answer this question and provide your reasoning in one or two sentences.
b) Summary statistics:
|
Column |
Mean |
Std. dev. |
|
Sample 6 (Time) |
48.33 |
10.50 |
Are these measures you found parameters or statistics in part (b) and why? Answer this question in one sentence?
Does the mean calculated in part (b) come from a sampling distribution that is approximately Normal? Check all three conditions of the Central Limit Theorem using one complete sentence for each condition to answer this question?
c) One sample T confidence interval:
μ: Mean of variable
95% confidence interval results:
|
Variable |
Sample Mean |
Std. Err. |
DF |
L. Limit |
U. Limit |
|
Sample 26 (Time) |
43.93 |
1.40 |
25 |
41.05 |
46.81 |
Calculate the probability in part (c) that, in a random sample of 26 students, the mean time to complete Exam 1 is 50 minutes or more. Complete this part by standardizing and using the Standard Normal Table to obtain this probability. Show all work and type all calculations?
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