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Hypothesis Test

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Q1


 !"#"#$%!$!!$&'(!$)!!%''"*"#+!&!$)!!'##"("*'*"&!$$&)"!"%!"!!'!!(+!,-./
0
120
120
130
12 0
120
12+0
Ans
1
43+Ho: Ud<=0
1
3+/Ho: Ud > 0
1
56+!6"+!6 8
1
 67862.7
1
+6+%*!9962.71:%(1
1
7+60.0131
Q2
;
7<=>?4!%('&#*)"!$!!!%
@<A345!'$"$!%&!($"&!%!)&"*!(!!!$")!$"
=/B3345!())*!!$!(%"#!%$)#"$!%"!$$!$!!!*
2:1
120

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Q1A school board is evaluating a learning system designed to increase literacy skills. A standardized test measuring reading skills is performed on some students, both before and after using the learning system. The following data were obtained:student before after difference 1 96 96 0 2 101 105 4 3 108 112 4 4 97 96 -1 5 108 114 6 6 93 97 4 7 95 100 5 8 91 92 1 9 114 113 -1 You want to answer the question: "Is there evidence that the learning system has increased the test scores?a) What is the null hypothesis?b) What is the alternative hypothesis?c) How may degrees of freedom are there?d) What is the sample standard deviation of the difference in the test scores?e) What is the value of the test statistic?f) What is the p-value?Ansa)Null Hypothesis - learning system has remains same or decreased the test scores , Ho: Ud<=0b)Alternative Hypothesis - learning system Increased the test scores , Ho: Ud > 0c)Degrees of freedom = n-1 = 9-1 = 8d)sample standard deviation of the difference in the test scores = Pooled Variance = 2.7e)Test-statistic to = -2.71 i.e | to | = 2.71 ( it lies between 2 to 3 )f)P-value of the test is = 0.0131Q2Measurements of ...
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