he following data represents grade point averages of 10 student-sample taken ran
ID: 3309796 • Letter: H
Question
he following data represents grade point averages of 10 student-sample taken randomly from a population of students. A claim was made of strict grading in a new Math Course. The claim indicates that students in this course make a point average of 2.3. Suppose you know that the standard deviation of Population GPA is 0.3, test this claim at 5% Type l error using the null hypothesis Ho: = 2.3 and answer the following question: The test statistic (three decimal places) is Student Grade 2.3 00D F4 FS F6 F9 F1OExplanation / Answer
Given that,
Standard deviation, =0.1449
Sample Mean, X =2.21
Null, H0: =2.3
Alternate, H1: !=2.3
Level of significance, = 0.05
From Standard normal table, Z /2 =1.96
Since our test is two-tailed
Reject Ho, if Zo < -1.96 OR if Zo > 1.96
Reject Ho if (x-2.3)/0.1449/(n) < -1.96 OR if (x-2.3)/0.1449/(n) > 1.96
Reject Ho if x < 2.3-0.284/(n) OR if x > 2.3-0.284/(n)
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Suppose the size of the sample is n = 10 then the critical region
becomes,
Reject Ho if x < 2.3-0.284/(10) OR if x > 2.3+0.284/(10)
Reject Ho if x < 2.21 OR if x > 2.39
Suppose the true mean is 2.3
Probability of Type I error,
P(Type I error) = P(Reject Ho | Ho is true )
= P(2.21 < x OR x >2.39 | 1 = 2.3)
= P(2.21-2.3/0.1449/(10) < x - / /n OR x - / /n >2.39-2.3/0.1449/(10)
= P(-1.964 < Z OR Z >1.964 )
= P( Z <-1.964) + P( Z > 1.964)
= 0.0248 + 0.0248 [ Using Z Table ]
= 0.05
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