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Chapter 8: Q. 9.56 (page 370)
We have given the P-value for a hypothesis test. For each exercise determine the strength of the evidence against null hypothesis.
Given
The P-value in this case is 0.06, which is higher than 0.10.
As can be seen from the conditions, there is some evidence against the null hypothesis.
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Heights of Supermodels Listed below are the heights (cm) for the simple random sample of female supermodels Lima, Bundchen, Ambrosio, Ebanks, Iman, Rubik, Kurkova, Kerr,Kroes, Swanepoel, Prinsloo, Hosk, Kloss, Robinson, Heatherton, and Refaeli. Use a 0.01 significance level to test the claim that supermodels have heights with a mean that is greater than the mean height of 162 cm for women in the general population. Given that there are only 16 heights represented, can we really conclude that supermodels are taller than the typical woman?
178 177 176 174 175 178 175 178 178 177 180 176 180 178 180 176
Test Statistics. In Exercises 13鈥�16, refer to the exercise identified and find the value of the test statistic. (Refer to Table 8-2 on page 362 to select the correct expression for evaluating the test statistic.)
16. Exercise 8 鈥淧ulse Rates鈥�
P-Values. In Exercises 17鈥�20, do the following:
a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.
b. Find the P-value. (See Figure 8-3 on page 364.)
c. Using a significance level of = 0.05, should we reject or should we fail to reject ?
The test statistic of z = -2.50 is obtained when testing the claim that
Cadmium, a heavy metal, is toxic to animals. Mushrooms, however, are able to absorb and accumulate cadmium at high concentrations. The Czech and Slovak governments have set a safety limit for cadmium in dry vegetables at part per million (ppm). M. Melgar et al. measured the cadmium levels in a random sample of the edible mushroom Boletus Pinicola and published the results in the paper "Influence of Some Factors in Toxicity and Accumulation of Cd from Edible Wild Macrofungi in NW Spain" (Journal of Environmental Science and Health, Vol. B33(4), pp. 439 455). Here are the data.
0.24 0.59 0.62 0.16 0.77 1.33
0.92 0.19 0.33 0.25 0.59 0.32
At the significance level, do the data provide sufficient evidence to conclude that the mean cadmium level in Boletus Pinicola mushrooms is greater than the government's recommended limit of ppm? Assume that the population standard deviation of cadmium levels in Boletus Pinicola mushrooms is 0.37 ppm.
(Note: the sum of the data is 6.31 ppm. )
Teacher Salaries. Refer to Exercise 9.22. Explain what each of the following would mean.
a. Type I error
b. Type II error
c. Correct decision
Now suppose that the results of carrying out the hypothesis test lead to nonrejection of the null hypothesis. Classify that conclusion by error type or as a correct decision if in fast the mean salary of classroom teachers in Ohio
d. equals the national mean of \(55.4 thousand.
e. exceeds the national mean of \)55.4 thousand.
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