Question

Question 29 3 pts Small Mean Problem. Grandfather clocks have a particular market in auctions. One theory about the price at an auction is that it is higher when there are 10 or more bidders. From published data, the average price of all grandfather clocks is given as $1,327. You are not given a standard deviation for all clocks. You are given a random sample of 14 purchases of grandfather clocks at auctions in Pennsylvania where there are 10 or more bidders. Assume your sample is random and approximately normal. The sample statistics are: Mean $1,491.43 Std Dev $411.53 CV 27.59 N 14 You are asked to test to see if the price is higher than $1,327 when there are 10 or more bidders. You will use alpha .05. If we changed the level of alpha to .10 for this hypothesis test, you would reject the Null Hypothesis. This is a true or false question. True False

Answer 1

29)

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 1327
Alternative Hypothesis: μ > 1327

Rejection Region
This is right tailed test, for α = 0.1 and df = 13
Critical value of t is 1.35.
Hence reject H0 if t > 1.35

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (1491.43 - 1327)/(411.53/sqrt(14))
t = 1.495

P-value Approach
P-value = 0.0794
As P-value < 0.1, reject the null hypothesis.

True

17)

sample mean, xbar = 19.45
sample standard deviation, s = 0.64
sample size, n = 15
degrees of freedom, df = n - 1 = 14

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.145

ME = tc * s/sqrt(n)
ME = 2.145 * 0.64/sqrt(15)
ME = 0.354

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (19.45 - 2.145 * 0.64/sqrt(15) , 19.45 + 2.145 * 0.64/sqrt(15))
CI = (19.10 , 19.80)

True, as the confidence interval does not contains 20