Question

# Consider the hypothesis statement shown below using alphaequals0.05 and the data to the right from two...

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.

• 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.

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