Solution Found!
(In some of the exercises that follow, we must
Chapter 8, Problem 5E(choose chapter or problem)
Some nurses in county public health conducted a survey of women who had received inadequate prenatal care. They used information from birth certificates to select mothers for the survey. The mothers selected were divided into two groups: 14 mothers who said they had five or fewer prenatal visits and 14 mothers who said they had six or more prenatal visits. Let \(X\) and \(Y\) equal the respective birth weights of the babies from these two sets of mothers, and assume that the distribution of \(X\) is \(N\left(\mu_{X}, \sigma^{2}\right)\) and the distribution of \(Y\) is \(N\left(\mu_{Y}, \sigma^{2}\right)\).
(a) Define the test statistic and critical region for testing \(H_{0}: \mu_{X}-\mu_{Y}=0\) against \(H_{1}: \mu_{X}-\mu_{Y}<0\). Let \(\alpha=0.05\).
(b) Given that the observations of \(X\) were
49 108 110 82 93 114 134
114 96 52 101 114 120 116
and the observations of \(Y\) were
133 108 93 119 119 98 106
131 87 153 116 129 97 110
calculate the value of the test statistic and state your conclusion.
(c) Approximate the \(p\)-value.
(d) Construct box plots on the same figure for these two sets of data. Do the box plots support your conclusion?
Equation Transcription:
Text Transcription:
X
Y
N(mu_X, sigma^2)
N(mu_Y, sigma^2)
H_0:mu_X-mu_Y=0
H_1:mu_X-mu_Y<0
alpha=0.05
p
Questions & Answers
QUESTION:
Some nurses in county public health conducted a survey of women who had received inadequate prenatal care. They used information from birth certificates to select mothers for the survey. The mothers selected were divided into two groups: 14 mothers who said they had five or fewer prenatal visits and 14 mothers who said they had six or more prenatal visits. Let \(X\) and \(Y\) equal the respective birth weights of the babies from these two sets of mothers, and assume that the distribution of \(X\) is \(N\left(\mu_{X}, \sigma^{2}\right)\) and the distribution of \(Y\) is \(N\left(\mu_{Y}, \sigma^{2}\right)\).
(a) Define the test statistic and critical region for testing \(H_{0}: \mu_{X}-\mu_{Y}=0\) against \(H_{1}: \mu_{X}-\mu_{Y}<0\). Let \(\alpha=0.05\).
(b) Given that the observations of \(X\) were
49 108 110 82 93 114 134
114 96 52 101 114 120 116
and the observations of \(Y\) were
133 108 93 119 119 98 106
131 87 153 116 129 97 110
calculate the value of the test statistic and state your conclusion.
(c) Approximate the \(p\)-value.
(d) Construct box plots on the same figure for these two sets of data. Do the box plots support your conclusion?
Equation Transcription:
Text Transcription:
X
Y
N(mu_X, sigma^2)
N(mu_Y, sigma^2)
H_0:mu_X-mu_Y=0
H_1:mu_X-mu_Y<0
alpha=0.05
p
ANSWER:Step 1 of 5
The test statistic for testing against is given by
Here, is the mean of values, is the mean of values.
is the pooled variance which will be calculated for populations with equal variances.
are the sample standard deviations.
The level of significance,
The critical value of t at corresponding to
significance level for a left tailed test,
Decision criterion:
If the test statistic value is less than , reject the .