Question

48 sample - 9 "0s" = 39	39 "1s" / 48 total sample=	0.8125
	pq=0.9*(1-0.9)	0.09
	pq/n= 0.09/48	0.001875
	sqrt (pq/n)= sqrt (0.001875)	0.043301
	sample prop / 90% =0.8125-0.9	-0.0875
	z=-0.0875/0.043301	-2.02073
	p value =NORMSDIST(H7)	0.02165

An air quality instrument logs 0 when standards are not met and 1 when standards are met. The log is saved to file DATA. First, compute the proportion meeting standards as the mean of air quality values. Second, at alpha=0.10 (sensitive, exploratory), test the hypothesis that proportion of times that air quality meets standards is at least 90%.

Time	Air Quality
0:00:00	1
0:00:30	1
0:01:00	1
0:01:30	1
0:02:00	1
0:02:30	1
0:03:00	1
0:03:30	1
0:04:00	1
0:04:30	1
0:05:00	1
0:05:30	1
0:06:00	1
0:06:30	1
0:07:00	1
0:07:30	1
0:08:00	1
0:08:30	0 (1)
0:09:00	0 (2)
0:09:30	0 (3)
0:10:00	1
0:10:30	1
0:11:00	1
0:11:30	0 (4)
0:12:00	1
0:12:30	0 (5)
0:13:00	1
0:13:30	0 (6)
0:14:00	1
0:14:30	1
0:15:00	0 (7)
0:15:30	1
0:16:00	0 (8)
0:16:30	1
0:17:00	1
0:17:30	0 (9)
0:18:00	1
0:18:30	1
0:19:00	1
0:19:30	1
0:20:00	1
0:20:30	1
0:21:00	1
0:21:30	1
0:22:00	1
0:22:30	1
0:23:00	1
0:23:30	1

Answer 1

Result:

An air quality instrument logs 0 when standards are not met and 1 when standards are met. The log is saved to file DATA. First, compute the proportion meeting standards as the mean of air quality values. Second, at alpha=0.10 (sensitive, exploratory), test the hypothesis that proportion of times that air quality meets standards is at least 90%.

Ho: P ≥ 0.9, H1: P < 0.9

This is a lower tail test.

single proportion test used.

calculated z = -2.0207

P=0.0217

Calculated P= 0.0217 < 0.10 level of significance.

The null hypothesis is rejected.

There is enough evidence to reject the claim that that proportion of times that air quality meets standards is at least 90%.

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis            p =	0.9
Level of Significance	0.1
Number of Items of Interest	39
Sample Size	48
Intermediate Calculations
Sample Proportion	0.8125
Standard Error	0.0433
Z Test Statistic	-2.0207
Lower-Tail Test
Lower Critical Value	-1.2816
p-Value	0.0217
Reject the null hypothesis