1. Identifying Hypotheses, Distributions, and Verifying Requirements Based on the given conditions, identify the alternative hypothesis. Also, either identify the sampling distribution

(normal, t, chi-square) of the test statistic, or state that the methods of this chapter should not be used.

Table 8-3 Hypothesis Tests Requirements: Distribution and Critical and Parameter Simple Random Sample and . . . Test Statistic P-Values Proportion np $ 5 and nq $ 5 Normal: Table A-2 Mean s known and normally Normal: Table A-2 or s known and n > 30 s not known and normally Student t: Table A-3 or s not known and n . 30 Population not normally Use a nonparametric method distributed and n # 30 or bootstrapping Standard Deviation Population normally distributed Chi-square: x2 5 Table A-4 sn 2 1ds2 s2 t 5 x 2 mx s

!n z 5 x 2 mx s

!n z 5 pˆ 2 p

Å

pq n

distributed population distributed population or Variance 446 Chapter 8 Hypothesis Testing

a. Claim: The mean annual income of full-time college students is below $10,000.

Sample data: For 750 randomly selected college students, the mean is $3662 and the standard deviation is $2996. The sample data suggest that the population has a distribution that is not normal.

b. Claim: The majority of college students have at least one credit card. Sample data: Of 500 randomly selected college students, 82% have at least one credit card.

c. Claim: The mean IQ of adults is equal to 100. Sample data: n 5 150 and It is reasonable to assume that s 5 15.

d. Claim: With manual assembly of telephone parts, the assembly times vary more than the times for automated assembly, which are known to have a mean of 27.6 sec and a standard deviation of 1.8 sec. Sample data: For 24 randomly selected times, the mean is 25.4 sec, the standard deviation is 2.5 sec, and the sample data suggest that the population has a distribution that is far from normal.

e. Claim: Statistics professors have IQ scores that vary less than IQ scores from the adult population, which has a standard deviation of 15. Sample data: For 24 randomly selected statistics professors, the standard deviation is 10.2, and the sample data suggest that the population has a distribution that is very close to a normal distribution.