Consider the following hypothesis test. H0: 1 - 2 0 Ha: 1 - 2 > 0 The following

ID: 3125350 • Letter: C

Question

Consider the following hypothesis test.

H0: 1 - 2 0
Ha: 1 - 2 > 0

The following results are for two independent samples taken from the two populations.

n1 = 40   n2 = 50
x¯1 = 25.2   x¯2 = 22.8
1 = 5.2   2 = 6.0

What is the value of the test statistic (round to 2 decimals)?

b. What is the p-value (round to 4 decimals)?

c. With = .05, what is your hypothesis testing conclusion?

p-value_________ H0 - Select your answer

-greater than or equal to 0.05, reject

-greater than 0.05, do not reject

-less than or equal to 0.05, reject

-less than 0.05, do not reject

-equal to 0.05, reject

-not equal to 0.05, reject

the null hypothesis and the alternative hypothesis is

H0: 1 - 2 0
Ha: 1 - 2 > 0

we have two independent samples, one from N(mu1,sigma12=5.22) and the other one from N(mu2,sigma22=62)

we have n1=first sample size=40 n2=second sample size=50

x1bar=first sample mean=25.2 x2bar=second sample mean=22.8

then we have the test statistic as

T=(x1bar-x2bar)/sqrt[5.22/n1+62/n2] which under H0 follows N(0,1)

so the value of test statistic=t=(25.2-22.8)/sqrt[27.04/40+36/50]=2.03 [answer]

b) since the alternative hypothesis is less than type

so p value=P[T<t]=P[T<2.03] where T~N(0,1)

=0.9788 [answer]

c) taking alpha=0.05

we have p value>alpha.

hence the correct alternative should be

greater than 0.05, do not reject [answer]

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