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Statistical Probabilities and Distributions

Homework for Prob./Dist. Lesson 12

  1. Find the value of t from the table which has a probability of 0.05 to the right of t when n=6.

     

     

     

  2. Use the table of t values to find a t value with probability of 0.99 to the right of t when n=21.

     

     

     

  3. What value of t would you use to find a 95% confidence interval for the mean of a population if n=16?

     

     

     

  4. Use tcdf on your calculator to find a t value for n=8 and a one-tailed alpha=0.005. You might start by comparing the results of tcdf(4.032,9E99,5) and tcdf(3.169,9E99,10) on your calculator with the corresponding entries in the table in the lesson.

     

     

     

  5. Suppose you have a one-sample t statistic from a sample of n=6. Suppose further that you calculated a t value of t=2.80 for your hypothesized population mean (H0: µ=64 and Ha: µ#64). Give the two-tailed probabilities which bracket this value. Calculate the P-value (twice the area to the right of this t value). Should you reject or fail to reject the null hypothesis?

     

     

     

     

    A university researcher placed 12 randomly selected radon detectors in a chamber that exposed them to 105 picocuries per liter of radon. The detector readings were as follows: 91.9, 97.8, 111.4, 122.3, 105.4, 95.0, 103.8, 99.6, 96.6, 119.3, 104.8, and 101.7.

  6. Construct a stem-and-leaf diagram of the above data using stems split two ways (i.e. 90-94, 95-99, ...). (Hint: it might be easier to round to integer first.)

     

     

  7. Check whether the sample size and skewness allow use of a t test.

     

     

  8. Calculate a t-value for the sample mean versus the population mean (105).

     

     

  9. Calculate the areas under the curve further away from the mean for this value of t (two-tailed). Is there convincing evidence that the mean reading of all detectors of this type differ from the true value?

     

     

  10. Calculate a two-sample t statistic for the data obtained from the 2000 penny experiment (mean=15.2, s.d.=2.71, n=18 for Calkins and mean=12.2, s.d.=1.39, n=9 for Burdick).

     

     

  11. Calculate the fractional degrees of freedom for the above penny experiment using the formula given at the end of the lecture on two-sample t tests. (n1=18 and n2=9). Compare this number with that obtained from the TI-83+ calculator STAT TESTS 4: 2-SampTTest ... not equal, not pooled, calculate.

     

     

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