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Hypothesis Z, t, C.I

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Statistics

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a-1. Calculate the value of the test statistic under the assumption that the population variances are unknown but equal. (Negative
values should be indicated by a minus sign. Round intermediate calculations to 4 decimal places and nal answer to 2 decimal places.)
Test Statistic
Given That X (Mean)=249
Standard Deviation (s.d1)=35
Number(n1)=10
Given That Y(Mean)=272
Standard Deviation(s.d2)=23
Number(n2)=10
Value of Combined Standard deviation is S= (n1*s1^2 + n2*s2^2 )/(n1+n2-2)
S = (10*1225 + 272*529) / (20- 2 )
S = 974.4444
we use Test Statistic (t) = (X-Y)/Sqrt(S^2(1/n1+1/n2))
t cal=249-272/Sqrt((949541.9753 ))
t cal=-23/13.9603
t cal=-1.6475
| t cal | =1.65
a-2.
Calculate the critical value at the 5% level of signicance. (Negative value should be indicated by a minus sign. Round your answer to 3
decimal places.)
The Value of |t tab| with (n1+n2-2) i.e 18 d.f is 1.729
a-3.
|t cal | < | t tab | and Here we Accept Ho
Yes, since the value of the test statistic is not less than the critical value.
t-Test for Dierence of the Population Means (Unequal Variances)
b-1.
Calculate the value of the test statistic under the assumption that the population variances are unknown and are not equal. (Negative
values should be indicated by a minus sign. Round intermediate calculations to 4 decimal places and nal answer to 2 decimal places.)
Test Statistic
Given That X(Mean)=249
Standard Deviation(s.d1)=35
Number(n1)=10
Given That Y(Mean)=272
Standard Deviation(s.d2)=23
Number(n2)=10
we use Test Statistic (t) = (X-Y)/Sqrt(s.d1^2/n1)+(s.d2^2/n2)
t cal=249-272/Sqrt((1225/10)+(529/10))
t cal=-1.7367
| t cal | =1.7367
b-2.
Calculate the critical value at the 5% level of signicance. (Negative value should be indicated by a minus sign. Round your answer to 3
decimal places.)
The Value of |t tab| with smaller value of (n1-1, n2-1) i.e 18 d.f is -1.833, +1.833
b-3. Do you reject the null hypothesis at the 5% level?
Make Decision
Hence Value of | t cal | > | t tab| and Here we Reject Ho
No, since the value of the test statistic is not less than the critical value.

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a-1. Calculate the value of the test statistic under the assumption that the population variances are unknown but equal. (Negative values should be indicated by a minus sign. Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.) Test Statistic Given That X (Mean) ...
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