Ch. 12–14 of Applied Statistics in Business and Economics

9.54

(a) At the .01 level of significance,is the true mean greater than 10?

Null Hypothesis: Ho: M = 10 :Mean is 10 or less pages
Alternative Hypothesis: H1: M >10 :Mean is more than 10 pages

Significance level=alpha (a) = 0.01 or 1%
No of tails= 1
This is a 1-tailed test because we are testing that the mean is greater than 10
Since sample size= 35 >= 30 we will use normal distribution

This is a one tailed test because we are testing the area in the right tail
Since the sample size is large we will use z distribution
Z at the 0.01 level of significance 1 tailed test = 2.3263 z critical= 2.3263

Decision rule

If the sample z value > z critical, 2.3263 reject Null Hypothesis
If the sample z value < z critical , 2.3263 accept Null Hypothesis

Alternatively:
If p value < significance level , 0.01 reject Null Hypothesis
If p value > significance level , 0.01 accept Null Hypothesis

Hypothesized Mean=M = 10 pages
Standard deviation =s= 4.45 pages sample size=n= 35 sx=standard error of mean=s/square root of n= 0.7522 = ( 4.45 /square root of 35) sample mean= 14.44 pages

z=(sample mean-M )/sx= 5.9027 =(14.44-10)/0.7522

Reject Null Hypothesis since z> z critical
The mean is greater than 10 pages

9.56
Null Hypothesis:Ho: p = 50.%
Alternative Hypothesis:H1: p > 50.%
Level of significance=alpha (a) = 0.10 or 10.0%

This is a one tailed test because we are testing the area in the right tail
Since the sample size is large we will use z distribution z critical= 1.2816

Decision rule

If the sample z value > z critical, 1.2816 reject Null Hypothesis
If the sample z value < z critical , 1.2816 accept Null Hypothesis

Alternatively:
If p value < significance level , 0.1 reject Null Hypothesis
If p value > significance level , 0.1 Accept Null Hypothesis

Decision rule: If the area in the right tails is less than the level of significance (0.10 0r