Question

Hi, I have a statistic question

Suppose you know that the weight of standard poodles is Normally distributed with a standard deviation of 5 pounds. You take an SRS of 8 poodles and find their average weight of 52 pounds

For the rest of this problem use the sample from before plus the following: Somebody tells you the average weight of standard poodles is 55 pounds.

(d) Run a two-sided significance test with a significance level of 5% to see if this person is correct or not.

(e) You have reason to believe this person is wrong, and that the average is actually smaller than they claim. Run the appropriate one-sided significance test with a significance level of 5%.

(f). Somebody else believes that this person is wrong and that the average is actually larger than the first person claimed. Run the appropriate one-sided significance test with a significance level of 5%.

(g). Compare your three answers above.

Answer 1

d) H₀: = 55

    H₁: 55

The test statistic z = ()/()

                             = (52 - 55)/(5/)

                             = -1.70

P-value = 2 * P(Z < -1.70)

             = 2 * 0.0446

             = 0.0892

As the P-value is greater than the significance level (0.0892 > 0.05), so we should not reject H₀.

e) H₀: = 55

    H₁: 55

The test statistic z = ()/()

                             = (52 - 55)/(5/)

                             = -1.70

P-value = P(Z < -1.70)

             = 0.0446

As the P-value is less than the significance level (0.0446 < 0.05), so we should reject H₀.

f) H₀: = 55

    H₁: 55

The test statistic z = ()/()

                             = (52 - 55)/(5/)

                             = -1.70

P-value = P(Z > -1.70)

              = 1 - P(Z < -1.70)

             = 1 - 0.0446

             = 0.9554

As the P-value is greater than the significance level (0.9554 > 0.05), so we should not reject H₀.

g) For two sided and for right tailed test, the null hypothesis is not rejected. . But for the left tailed test, the null hypothesis is rejected.