Question

Asked Nov 4, 2019

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Various temperature measurements are recorded at different times for a particular city. The mean of 20°C is obtained for 40 temperatures recorded on 40 different days. Assuming that the standard deviation is 1.5°C, test the claim that the population mean is 22°C. Use a 0.05 significance level.

Step 1

The hypotheses for the test is given below:

*Null hypothesis:*

*H*_{0}: *µ* = 22.

*Alternative hypothesis:*

*H*_{1}: *µ* ≠22.

*Test statistic for t-test:*

Since population standard deviation is unknown, the appropriate test is one sample *t-*test.

Step 2

Here, the sample mean, *x*-bar is 20.

Population mean, *µ* is 22.

Sample standard deviation, *s* = 1.5.

Sample size, *n* is 40.

The test statistic for *t*-test is calculated as given below.

Step 3

The test statistic value is **–8.439**.

*Computation of P-value:*

The two tailed *P*-value for the *t*-test at 39 degrees of freedom is approximately 0 whic...

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