- 14.1
- a) The sampling distribution of x
is Normal with mean 12 g/dl and standard deviation .226 g/dl.
- 14.3 H0: μ=12 g/dl. The mean hemoglobin
level for Jordanian children is 12 g/dl.
Ha: μ < 12 g/dl. The mean hemoglobin level for
Jordanian children is less than 12 g/dl.
- 14.5 H0: μ=26 mpg. The mean consumption of
fuel on the highway is 26 mpg.
Ha: μ > 26 mpg. The mean consumption of fuel on
the highway is greater than 26 mpg.
- 14.7 The test statistic for x= .3 is
(.3-0)/.316 = .95.
- 14.8 The test statistic for 11.3 g/dl is (11.3-12)/.226 =
-3.09. The test statistic for 11.8 g/dl is (11.8-12)/.226= -.884.
- 14.10 Using the results of 14.7, the test statistic is
.09. The p-value for this is .1711.
- 14.11 The p-value for the test statistic -3.09 is .001.
The p-value for the test statistic -.884 is .1894. The p-value for
-3.09 (the test statistic for 11.3 g/dl) indicates that it is very
unlikely to have seen similar results if the null hypothesis is true (
around 1 time in 1000). The p-value for -.88 (the test statistic for
11.8 g/dl) indicates that it is not so unlikely to have seen similar
results if the null hypothesis is true.
- 14.14 The sample average of 11.8 in the anemia study is not
statistically different than 12 at the .05 or the .01 levels.
- 14.17 the test statistic for the observed mean is
(4.62-5)/.137 = -2.77. The p-value is .0028, so this is strong evidence
that the stream has a mean oxygen content of less than 5mg per liter.
- 14.21 The significant values of the z-statistic for a
upper one-sided test with α=.005 are z≥ 2.58.
- 14.25
- a) You cannot reject the null hypothesis that μ=34 at
the 5% significance level because 34 is within the 95% confidence
interval for the population mean.
- b) You can reject the null hypothesis that μ=36 at the
5% significance level because 36 is not within the 95% confidence
interval for the population mean.
- 14.28 The sample average is 30.4. The test statistic
for this value under the null hypothesis that the mean is 25 is
(30.4-25)/2.21 = 2.44. The p-value for an upper one-sided test is
.0207. This is strong evidence that the mean threshold for untrained
tasters is greater than 25.
- 14.32 H0: μ=μ0. The mean
response with the placebo is the same as the mean response with no
treatment.
Ha: μ<μ0. The mean response with
the placebo is less than the mean response with no treatment.
- 14.33 Based on the results stated, it is very unlikely that
the placebo has no effect, so it is reasonable to reject the null
hypothesis that the mean resopnse of the placebo is the same as the
mean response for no treatment.
- 14.35
- a) The p-value for the upper one-sided hypothesis is .0359.
- b) The p-value for the lower one-sided hypothesis test is
.9641.
- c) The p-value for the two-sided hypothesis test is .0718.
- 14.39 The fact that P=0.02 implies that the chances of the
results seen in the experiment being due entirely to chance assignment
of patients is only 2%.
- 14.42 Under the null hypotheses of "no change" the probability
of seeing results more extreme than those observed is .62 and .98. This
means that random variablility is an adequate explanation for the observed
data.