Question

Consider the hypothesis statement shown below using alphaequals0.05 and the data to the right from two independent samples.
Upper H 0 : mu 1 minus mu 2 greater than or equals 0
Upper H 1 : mu 1 minus mu 2 less than 0
?a) Calculate the appropriate test statistic and interpret the result.
?b) Calculate the? p-value and interpret the result.

x overbar1
equals
121
x overbar2
equals
137
sigma1
equals
40
sigma2
equals
34
n1
equals
45
n2
equals
55
?

a) The test statistic is
nothing.
?(Round to two decimal places as? needed.)
Determine the appropriate critical? value(s).
The critical? value(s) is(are)
nothing.
?(Round to three decimal places as needed. Use a comma to separate answers as? needed.)

Since the test statistic
?
does not fall
falls
in the rejection? region,
?
reject
do not reject
Upper H 0. There is
?
sufficient
insufficient
evidence to conclude that the mean of population 1 is less than the mean of population 2.
?

b) The? p-value is
nothing.
?(Round to three decimal places as? needed.)

Since the? p-value is
?
less than
greater than
equal to
alpha?,
?
reject
do not reject
Upper H 0. There is
?
sufficient
insufficient
evidence to conclude that the mean of population 1 is less than the mean of population 2.

Answer 1

• Here we have to test the claim that mean of population 1 is less than mean of population 2
• HYPOTHESIS TO BE TESTED
• Ho: vs H1:
• TEST STATISTICS IS GIVEN BY
• 
• Now by substituing the mean and standard deviation test statistics obtained is
• =-2.127
• P-VALUE
• P(Z<-2.127)=1-P(Z<2.127)
• =1-0.98300 (i.e the associatied p value with the z value from the normal distribution table)
• =0.017
• Therefor the p value obtained is less than 5% significant level.
• Therefore we have enough evidence to reject the null hypothesis
• Thereofre we conclude that mean of population 1 is less than mean of population 2.