want to be engineers differs from the mean IQ of all girls in this age range.Notes on the above solution:
• Had the alternative hypothesis been one-sided, the P -value would have been 1 – 0.9821 = 0.0179. We
multiplied by 2 in step III because we needed to consider the area in both tails.
• The problem told us that the significance level was 0.05. Had it not mentioned a significance level, we
could have arbitrarily chosen one, or we could have argued a conclusion based only on the derived P -
value without a significance level.
• The linkage between the P -value and the significance level must be made explicit in part IV. Some sort
of statement, such as “Since P = 0.0358 < α = 0.05 ...” or, if no significance level is stated, “Since the
P -value is low ...” will indicate that your conclusion is based on the P -value determined in step III.
Calculator Tip: The TI-83/84 can do each of the significance tests described in this chapter as well
as those in Chapters 13 and 14 . It will also do all of the confidence intervals we considered in
Chapter 11 . You get to the tests by entering STAT TESTS . Note that Z-Test and T-Test are what are
often referred to as “one-sample tests.” The two-sample tests are identified as 2-SampZTest and 2-
SampTTest . Most of the tests will give you a choice between Data and Stats . Data means that you
have your data in a list and Stats means that you have the summary statistics of your data. Once you
find the test you are interested in, just follow the calculator prompts and enter the data requested.solution 2 (confidence interval approach—ok since H (^) A is two-sided, but not recommended):
I. Let μ = the true mean IQ of girls who want to be engineers.
H 0 : μ = 100.
H (^) A : μ ≠ 100.
II. We will use a 95% z -confidence interval (C = 0.95).
Conditions:
• We have a large sample size (n = 49).
• The standard deviation is known (σ = 15).
III. = 104.5, z * = 1.96.
We are 95% confident that the true population mean is in the interval (100.3, 108.7).
IV. Because 100 is not in the 95% confidence interval for μ , we reject H 0 . We have strong