Question

Section 8.3: Testing Hypotheses. In Exercises 9-24, 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 bypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), critical value(s), and state the final conclusion that addresses the original claim. 12. Discarded Plastic The weights (lb) of discarded plastic from a sample of households is listed in Data Set 23 in Appendix B, and the summary statistics are n = 62, x = 1.911 Ib, and s = 1.065 lb. Use a 0.05 significance level to test the claim that the mean weight of discarded plastic from the population of households is greater than 1.800 lb. 32. Repeat Exercise 12 assuming that the population standard deviation or is known to be 1.065 lb. 14. Human Body Temperature Data Set 3 in Appendix B includes a sample of 106 body temperatures with a mean of 98.20°F and a standard deviation of 0.62°F. Use a 0.05 sig- nificance level to test the claim that the mean body temperature of the population is equal to 98.6°F, as is commonly believed. Is there sufficient evidence to conclude that the common belief is wrong?

Answer 1

#12.
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 1.8
Alternative Hypothesis, Ha: μ > 1.8

Rejection Region
This is right tailed test, for α = 0.05 and df = 61
Critical value of t is 1.67.
Hence reject H0 if t > 1.67

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (1.911 - 1.8)/(1.065/sqrt(62))
t = 0.821

P-value Approach
P-value = 0.2074
As P-value >= 0.05, fail to reject null hypothesis.

#32.
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 1.8
Alternative Hypothesis, Ha: μ > 1.8

Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.64.
Hence reject H0 if z > 1.64

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (1.911 - 1.8)/(1.065/sqrt(62))
z = 0.82

P-value Approach
P-value = 0.2061
As P-value >= 0.05, fail to reject null hypothesis.

#14.
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 98.6
Alternative Hypothesis, Ha: μ ≠ 98.6

Rejection Region
This is two tailed test, for α = 0.05 and df = 105
Critical value of t are -1.983 and 1.983.
Hence reject H0 if t < -1.983 or t > 1.983

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (98.02 - 98.6)/(0.62/sqrt(106))
t = -9.631

P-value Approach
P-value = 0
As P-value < 0.05, reject the null hypothesis.

Yes the belief is wrong