Question

Problem #1 - Using Excel

A healthcare consultant wants to compare the patient satisfaction ratings of two hospitals. The consultant collects ratings from 20 patients for each of the hospitals as listed in column A and column B of this data sheet.

The consultant wants determine whether there is a difference in the patient ratings between the hospitals. The population standard deviations for the ratings are known to be 8 for Hospital A and 10 for Hospital B.

Use a 0.05 significance level and fill out each of the following blank cells to reach your conclusion. Use the Excel "Data Analysis" ToolPak to calculate the necessary statistics.

Hospital A	Hospital B
81	89
77	64
75	85
74	78
86	89
90	85
62	87
73	77
91	82
98	79
81	69
85	78
77	65
78	71
83	77
90	88
78	73
76	68
71	75
80	80

Step 1	Develop Hypotheses
	H0:
	Ha:
Step 2	Specify the Significance Level (a)
	a=
Step 3	Compute the Test Statistic
	Test Statistic =
Step 4	Determine the Critical Value
	Critical Value =
Step 5	Compute the p-value
	p-value
Step 6	Make your decision whether to reject H0 or not
	p-value vs. a
	Test statistic vs. Critical value
	Decision
Step 7	Interpret the statistical conclusion

Answer 1

Given that,
mean(x)=80.3
standard deviation , sigma1 =8
number(n1)=20
y(mean)=77.95
standard deviation, sigma2 =10
number(n2)=20
null, Ho: u1 = u2
alternate, H1: μ1 != u2
level of significance, alpha = 0.05
from standard normal table, two tailed z alpha/2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
zo=80.3-77.95/sqrt((64/20)+(100/20))
zo =0.82
| zo | =0.82
critical value
the value of |z alpha| at los 0.05% is 1.96
we got |zo | =0.821 & | z alpha | =1.96
make decision
hence value of | zo | < | z alpha | and here we do not reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 0.82 ) = 0.41184
hence value of p0.05 < 0.41184,here we do not reject Ho
------------------------------------------------------------------------------
null, Ho: u1 = u2
alternate, H1: μ1 != u2
test statistic: 0.82
critical value: -1.96 , 1.96
decision: do not reject Ho
p-value: 0.41184
no evidence to support that there is a difference in the patient ratings
between the hospitals