Hypothesis Test A. The average maximum temperature in San Francisco for the mont
ID: 3130362 • Letter: H
Question
Hypothesis Test
A. The average maximum temperature in San Francisco for the month of December is 58°F with a population standard deviation of 6°F. A random sample of 12 days taken in the month of December 2012 yielded an average maximum temperature of 55°F. Assume a normally distributed population. Test using the critical value method if the population mean maximum temperature in San Francisco for the month of December has decreased from 58°F, using = 0.05.
B. The Pew Research Center reported that 73% of Americans who own a cell phone also use text messaging. In a recent local survey, 387 out of 500 cell phone owners used text messaging. Since a Z test is appropriate, test whether the population proportion of Americans who use text messaging is different from 73%. Use level of significance = 0.10.
C. Random samples of 10 fish were given a hormone treatment after which the blood calcium was measured (mg Ca/100 ml blood). The data are given below. We are interested in whether the population standard deviation of the blood calcium is different from 1.0, using a level of significance = 0.05. 16.87 14.92 15.63 16.83 17.19 15.86 16.18 17.12 15.24 14.80
Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u >= 58
Ha: u < 58
As we can see, this is a left tailed test.
Thus, getting the critical z, as alpha = 0.05 ,
alpha = 0.05
zcrit = - 1.644853627
Getting the test statistic, as
X = sample mean = 55
uo = hypothesized mean = 58
n = sample size = 12
s = standard deviation = 6
Thus, z = (X - uo) * sqrt(n) / s = -1.732050808
As |z| > 1.6449, we REJECT THE NULL HYPOTHESIS.
Hence, there is significant evidence at 0.05 level that he population mean maximum temperature in San Francisco for the month of December has decreased from 58°F. [CONCLUSION]
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