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Chapter 8: Q. 9.57 (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 is 0.06, which is in the range of 0.01 to 0.05.
As a result, the null hypothesis is strongly discounted.
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Critical Values. In Exercises 21–24, refer to the information in the given exercise and do the following.
a. Find the critical value(s).
b. Using a significance level of = 0.05, should we reject or should we fail to reject ?
Exercise 19
Type I and Type II Errors. In Exercises 29–32, provide statements that identify the type I error and the type II error that correspond to the given claim. (Although conclusions are usually expressed in verbal form, the answers here can be expressed with statements that include symbolic expressions such as p = 0.1.).
The proportion of people who write with their left hand is equal to 0.1.
Testing Hypotheses. In Exercises 13–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.
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
Testing Hypotheses. In Exercises 13–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.
Car Booster Seats The National Highway Traffic Safety Administration conducted crash tests of child booster seats for cars. Listed below are results from those tests, with the measurements given in hic (standard head injury condition units). The safety requirement is that the hic measurement should be less than 1000 hic. Use a 0.01 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified requirement?
774 649 1210 546 431 612
Final Conclusions. In Exercises 25–28, use a significance level of = 0.05 and use the given information for the following:
a. State a conclusion about the null hypothesis. (Reject or fail to reject .)
b. Without using technical terms or symbols, state a final conclusion that addresses the original claim.
Original claim: The standard deviation of pulse rates of adult males is more than 11 bpm. The hypothesis test results in a P-value of 0.3045.
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