Mathematics

Question

A large software company gives job applicants a test of programming ability and the mean for that test has been 160 in the past. twenty-five job applicants are randomly selected from one large university and they produce a mean score and standard deviation of 183 and 12, respectively. use a 0.05 level of significance to test the claim that this sample comes from a population with a mean score greater than 160.

2 Answer

  • See attachment for answer.
  • Step-by-step explanation:

    Mean of the test of programming ability was 160 in the past.

    Again now, twenty-five job applicants are randomly selected from one university and they produce a mean score and standard deviation of 183 and 12.

    So in this case, the null hypothesis will be,

    [tex]H_o: \mu = 160[/tex]

    and alternate hypothesis will be,

    [tex]H_a: \mu > 160[/tex]

    Mean of the sample = [tex]\overline{x}[/tex] = 183

    Standard deviation of the sample = [tex]\sigma[/tex] = 12

    sample size = n = 25

    Using t distribution,

    [tex]t=\dfrac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

    [tex]=\dfrac{183-160}{\frac{12}{\sqrt{25}}}[/tex]

    [tex]=9.58[/tex]

    P-value =[tex]P(t > 9.58)\approx 0[/tex]

    As the obtained value is less than 0.05 or 5% level of significance, so we have to reject the null hypothesis.

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