Question

In: Statistics and Probability

Small Mean Problem. Grandfather clocks have a particular market in auctions.   One theory about the price...

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 20 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 = 20

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 fail to reject the Null Hypothesis.  This is a true or false question.

Solutions

Expert Solution

[OR]

Answer:

Given that, sample size (n) = 14

sample mean = $1491.43

sample standard deviation (s) = $411.53

The null and alternative hypotheses are,

H0 : μ = $1327

Ha : μ > $1327

Using TI-83 plus calculator we get,

Test statistic = t = 1.495

P-value = 0.0794

Therefore, if we changed the level of alpha to 0.10 for this hypothesis test, the p-value = 0.0794 < alpha = 0.10, so we should reject the null hypothesis.

Hence, this is a True statement.

Answer : True

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