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 • C.V. = 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 O False Question 30 3 pts Proportion Problem. Each year Delta Dental does a survey of parents concerning the tradition of the Tooth Fairy. A random sample of 1,058 parents were asked about how much money they leave for a tooth and questions concerning how their child responded to the concept of the Tooth Fairy. In one question, 508 parents indicated that their child saved the money they got for their tooth. You are asked to calculate a 99% Confidence Interval for this proportion. What is the standard error you will use in this Confidence interval? I just want the answer. Use 4 decimal places for your answer and use the proper rules of rounding.

Answer 1

#29.
False

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

Rejection Region
This is right tailed test, for α = 0.05 and df = 13
Critical value of t is 1.771.
Hence reject H0 if t > 1.771

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 >= 0.05, fail to reject null hypothesis.

#30.
sample proportion, pcap = 508/1058 = 0.4802
sample size, n = 1058

Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.4802 * (1 - 0.4802)/1058) = 0.0154