High School

School administrators claim that the mean number of students who eat cafeteria food daily is 173. A statistics class at this school feels this claim is high, and a t-test is performed on H0: μ = 173 versus Ha: μ < 173, where μ is the true mean number of students who eat cafeteria food daily at this school. The resulting P-value is 0.032. What conclusion should be made at the α = 0.05 level?

Answer :

To address the question of whether the mean number of students who eat cafeteria food daily at the school is less than the administrators' claim of 173, we can analyze the statistical test results provided.


  1. Hypotheses:


    • Null Hypothesis ([tex]H_0[/tex]): [tex]\mu = 173[/tex] (The true mean number of students who eat cafeteria food daily is 173.)

    • Alternative Hypothesis ([tex]H_a[/tex]): [tex]\mu < 173[/tex] (The true mean number of students who eat cafeteria food daily is less than 173.)



  2. Significance Level:


    • The significance level ([tex]\alpha[/tex]) is 0.05. This is the threshold for deciding whether the results are statistically significant, meaning unlikely to have occurred by random chance.



  3. P-Value:


    • The calculated P-value from the t-test is 0.032.



  4. Decision Rule:


    • If the P-value is less than the significance level [tex]\alpha = 0.05[/tex], we reject the null hypothesis.



  5. Conclusion:


    • Since the P-value (0.032) is less than [tex]\alpha[/tex] (0.05), we reject the null hypothesis.

    • This means there is sufficient statistical evidence at the 0.05 level to conclude that the mean number of students who eat cafeteria food daily is less than 173.




In summary, the statistics class's suspicion that the average number of students eating cafeteria food is lower than the claimed 173 is supported by the data at the 0.05 significance level.

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