What is the critical value t* that satisfies the condition that the t distribution with 8 degrees of freedom has probability 0.10 to the right of t*? From Table

8.   What is the critical value t* that satisfies the condition that the t distribution with 8 degrees of freedom has probability 0.10 to the right of t*? From Table

(a)  1.397               (b) 1.282                      (c) 2.89                        (d) 0.90

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(e)  None of the above.  The answer is                                                          .

Part 2:            Free Response

Communicate your thinking clearly and completely.

9.   You measure the weights of 24 male runners. You do not actually choose an SRS, but you are willing to assume that these runners are a random sample from the population of male runners in your town or city. Here are their weights in kilograms:

67.8     61.9     63.0     53.1     62.3     59.7     55.4     58.9

60.9     69.2     63.7     68.3     64.7     65.6     56.0     57.8

66.0     62.9     53.6     65.0     55.8     60.4     69.3     61.7

(a) Construct and interpret a 95% confidence interval for , the mean of the population from which the sample is drawn.

The population of interest is all male runners in our town.  We want to estimate the µ, the mean weight of male runners in our town.

Since we do not know σ, we should construct a t-interval for the mean weight µ if the conditions are satisfied.

SRS: the data comes from a SRS in the information above

Normality: The box plot of the data does not contain outliers or have strong skewness. The histogram of the sample is somewhat symmetrical with one single mound.  The probability plot has some curvature on the ends and quite linear though the middle.  I have no concerns about the normality of the population distribution of male runner weights.

n = 24, x-bar = 61.792, sx-bar = 4.81

=  = (59.762, 63.822)

(b)   Explain the meaning of 95% confidence in part (a).

We are 95% confident that the true mean weight for male runners in our town is between 59.76 kg and 63.82 kg.