Question
Various temperature measurements are recorded at different times for a particular city. The mean of 20 degree C is obtained for 40 temperatures on 40 different days. Assuming that sigma = 1.5 degree C, test the claim that the population mean is 23 degree C. Use a 0.05 significance level. Test the given claim. Use the P-value method or the traditional method as indicated. Identify the null hypothesis, alternative hypothesis, test statistic, critical value(s) or P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. A simple random sample of 15-year old boys from one city is obtained and their weights (in pounds) are listed below. Use a 0.01 significance level to test the claim that these sample weights come from a population with a mean equal to 149 lb. Assume that the standard deviation of the weights of all 15-year old boys in the city is known to be 162 lb. Use the traditional method of testing hypotheses. 147 138 162 151 134 189 157 144 175 127 164
Explanation / Answer
Null Hypothesis (Ho): µ = 23
Alternative Hypothesis (Ha): µ ¹ 23
The level of significance = .05
Test Statistics: z = (x bar - µ) / (s/sqrt(40))
= (20-23)/(1.5/sqrt(40))
= -12.65
p-value = 2 * P (z <-12.65)
= 2 * 0.0000 [ From Normal Distribution Table]
= 0.0000
p-value is less than the level of significance (.0000<.05); we reject the null hypothesis.
At 5% level of significance there is not sufficient evidence to conclude that the population mean is 23 degrees centigrade.
