 # To state:Null hypothesis and alternative hypothesis. hexacordoK 2020-11-14 Answered
To state:Null hypothesis and alternative hypothesis.
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Given:
A professor is concerned that the two sections of college algebra that he teaches are not performing at the same level. To test his claim, he looks at the mean exam score for a random sample of students from each of his classes. In Class1, the mean exam for 12 students is 78.7 with a standard deviation of 6.5. In Class 2, the mean exam core for 15 students is 81.1 with a standard deviation of 7.4. Assume that the population variances are equal.
Let class 1 is population! and class 2 is population 2. Let ${\mu }_{1}$ be the mean exam score of population 1 and ${\mu }_{2}$ mean score of population 2. A professor is concerned that the two sections of college algebra that he teaches are not performing at the same level. When written mathematically, this is ${\mu }_{1}\ne {\mu }_{2}$ and hence the alternative hypothesis. By subtracting ${\mu }_{2}$ from both sides of the above inequality result $i{\mu }_{1}i-{\mu }_{2}0$.
The null hypothesis is that there is no significant difference between the mean exam scores of class 1 and class 2 students.
${H}_{0}:{\mu }_{1}-{\mu }_{2}=0$
Alternative hypothesis is that there is a significant difference between the mean exam scores of class 1 students and class 2 students.
${H}_{1}:{\mu }_{1}-{\mu }_{2}\ne 0$
Thus, the hypotheses are stated as follows: ${H}_{0}:{\mu }_{1}-{\mu }_{2}=0$
${H}_{1}:{\mu }_{1}-{\mu }_{2}\ne 0$