statistics homework

I. Answer T (true) or F (false).

 

  1. For a normally distributed population of heights of 10,000 women, m = 63 inches and s = 5 inches.

      The number of heights in the population that fall between 66 and 68 inches is 1156.

 

         2. In a normal distribution, approximately 91.31% of the area under the curve is found to the right of a

             point -1.36 standard deviations from the mean.

 

         3. Approximately 92.5% of the area under the normal curve is located between the mean and

             +/- 1.78 standard deviations from the mean.

 

         4. Given a normal population with m = 125, s = 15 and n = 25, the P(x-bar > 127) = 0.2514.

 

         5. If floodlight life is normally distributed with mean 3500 hours and standard deviation of 200 hours,

             then the proportion of those lasting longer than 4000 hours is 0.062.

 

         6. It is correct to say that the standard error of the mean is also the standard deviation of a

             sampling distribution of means.

 

         7. P(-0.5 < Z < -0.3) = 0.0736.

 

         8. For normally distributed I.Q.’s with mean of 100 and standard deviation of 16, the probability that 25

             randomly selected individuals have an average I.Q. less than 95 is 0.0594.

 

         9. The standard error of a sampling distribution of means will sometimes be larger than the standard

            deviation of the population upon which the sampling distribution is based.

 

        10. With s remaining constant, decreasing the sample size causes a smaller standard error.

 

        11. As n increases, the width of a confidence interval for m increases, assuming s is constant.

 

        12. If P(Z > z) = 0.67, then z = -0.44.

 

        13. Given n = 100 and s^2 = 100, the estimate of the standard error of the mean is 10.

 

        14. Given a sample with n = 100, H0 : m = 500, HA : m ¹ 500, and a = 0.05, the null hypothesis can be

              rejected if and only if z  ³ 1.645 or z £ -1.645.

 

        15. In problem 14, if x-bar = 505 and s = 20, the null hypothesis cannot be rejected with p = 0.062.

 

        16. A Type II error results from the failure to reject a true null hypothesis, and a Type I error

              results from rejecting a false null hypothesis.

 

        17. If n = 12, x-bar = 43 and s = 3.5, then a 95% confidence interval for m is 40.776 to 45.224.

 

        18. John weighs 165 pounds and George weighs 190 pounds.  It is correct to state that a

              statistically significant difference exists between the weights of John and George.

 

        19. The critical value of t required to reject a null hypothesis at a given a-level is smaller for a two-

               tailed test than for a one-tailed test.

 

        20. A 98% confidence interval for n =12, x-bar = 48.9 and s = 9.1 is 48.9 +/- 8.16.

 

        21. When performing hypothesis tests or computing confidence intervals based on large samples,

               it is not necessary to assume that the data in the parent population(s) are distributed normally.

 

        22. To estimate m within two units with 95% confidence and s = 10 requires n be at least 96.

 

        23. When working with a sample size of n = 9, assuming a one-tailed test, more than 5% of the

              area under the appropriate t-curve will be located in the tail beyond 1.65 standard errors.

 

        24. If a two-tailed test assumes a 5% rejection region, then the total rejection region is 10%; that

              is, it consists of 5% in each tail.

 

        25. The p-value for a hypothesis test resulting in z > 2.63 is approximately 0.0034.

 

        26. “Statistical significance” may be defined as the rejection of a null hypothesis at some a-level.

 

        27. A 90% confidence interval for a sample of 50 funds with x-bar =12.9% and s = 3% is 12.9 +/- 0.7%.

 

        28. If 15-minute coffee breaks are given, then the random sample, 12,16,14,18,21,17,15,19,18,16,

              statistically substantiates at the 5% significance level that coffee breaks are longer than allowed.

        

        29. In the hypothesis test, Ho:p = 0.10, Ha:p ¹ 0.10, x = 27 & n = 200, the p-value is 0.099.

 

        30. Different, significantly different and statistically significantly different have the same meaning.

 

        31. At 5% significance the fail to reject test statistic for Ho:(m1-m2) = 0, Ha:(m1-m2) < 0, n1 = 8,

              n2 = 8, x1-bar = 53.6, x2-bar = 61.5, s1 = 12.5 and s2 = 10.6 is t = -1.36.

 

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Answer:

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    * T
    2
    ** *
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    * T
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    F *
    T
    * F
    8
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    11
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    13 **
    14
    F 15
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    ** F
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    19 **
    20
    ** **
    **
    ** F
    **
    ** 24 T
    **
    ** ** **
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    F **
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