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The average temperature in a large refrigerated room should not exceed 1.5 oC. Over an appropriate...

The average temperature in a large refrigerated room should not exceed 1.5 oC. Over an appropriate length of time, the temperature is measured 12 times; the sample mean is found to be 1.68oC with a sample standard deviation of 0.81oC. Does this result strongly suggest that the true mean temperature is greater than 1.5 oC? Solve this question by using hypothesis testing

math   Statistics-And-Probability   
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Answer #1

H0: \mu <= 1.5oC

Ha: \mu > 1.5oC (Right tailed)

Test statistics

t = \bar{x} - \mu / S / sqrt(n)

= 1.68 - 1.5 / 0.81 / sqrt(12)

= `0.77

This is test statistics value.

Critical value at 0.05 significance level for 11 df is 1.796

Since calculated test statistics value < 1.796, we do not have sufficient evidence to reject H0.

We conclude that, we fail to support the claim that true mean temperature is greater than 1.5oC.

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