Question

2 HW#9 - Chapter 18 (20pts for turned in on time) (12pts Body weight for students in NMSU is Normal distributed in a report stated that the average weight for NMSU students is about 160 pounds. Aresearcher read the report, and he suspect that the average weight is below 160 pounds. To t he collected a SRS of 25 students from NMSU and the sample mean is 156 3 pounds, with a standard deviation of 12 pounds (1) (6pts)Suppose you know the population standard deviation of NMSU students is 10 pounds perform an appropriate test to do the analysis on 0.05 significance level. Choose between test and t test). a - Ho: M = 160 Hoiu2160 b - PL0.05 c-2: 156.3 - 160 = -1.85 olun tolas d - -P(2=.6322) Lal=0.05) - reject null hypothesis { We have enough. evidca that average weight is below 160 pands. (2) (6pts)Suppose you DON'T know the population standard deviation, perform an appropriate test to do the analysis at 0.05 significance level. (Choose between z test or t test) 9 Holl = 160 Ha L160 bp20.05 156.3-166 ctx-M s/n -1.54 dlf = 24 - 2.0.05 Pitk-1.54) = 0,05 > 1.54 10 0s.

Answer 1

The z-test is appropriately used in the first part of the question. THe solution seems perfect.

(2) Here, we will be using t-test as the population standard deviation is not known.

Ho: mu = 160
Ha: mu < 160

The t-statistic calculated = -1.54
df = 25 - 1 = 24

From the t-table at df = 24, p-value (one-tailed) = 0.0683

p-value > 0.05, We fail to rejcet the null hypothesis at a significance level of 0.05

E - We do not have enough evidence that the average weight is below 160 pounds