the 2 You rooms in the basement if taking a building, in a room without windows,

Question

the 2 You rooms in the basement if taking a building, in a room without windows, such as some of the spread of the scores. Over last years, in of the Cc exam omly with windows, two d a sample 29 exams take calculus exam scores been n (78. 2.10.8). You ran standard in hav find a sample average of 75.3 the deviation of 13.8. windowless rooms and does it seem as though exam are affected At evel of significance, room? by taking the exam in a windowless Hypothesis Null Hypot Alternativ Critical Critical Test

Explanation / Answer

Null hypothesis: H0: µ = 78.2

Alternative Hypothesis: Ha: µ 78.2

This is a two tailed test.

Critical values = 2.1539 and -2.1539

Critical Region: |t| > 2.1539

We are given Xbar = 75.3, S = 13.8, sample size n = 29

Test value = t = (Xbar - µ) / [S/sqrt(n)] = (75.3 – 78.2) / [13.8/sqrt(29)] = -1.1317

P-value = 0.2674

Alpha value = 0.04

Statistical Decision: Do not reject the null hypothesis H0

Justification for decision: P-value > Alpha value

Decision in contextual terms: We concluded that there is sufficient evidence that the spread of the exam scores does not affected by taking the exam in a windowless room.

Justification for Distribution used

For the given scenario, we do not given the population standard deviation and also sample size is small, so we use the t distribution. If we are given the population standard deviation and usually sample sizes are larger, then we use the Z or normal distribution.

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