Test the given claims using the traditional method of hypothesis testing. 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.

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Asked Nov 4, 2019

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Test the given claims using the traditional method of hypothesis testing.

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.

Expert Answer

Step 1

The hypotheses for the test is given below:

Null hypothesis:

H₀: µ = 22.

Alternative hypothesis:

H₁: 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.

Image Transcription
n 20 22 1.5 40 -2 0.237 8.439

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...

Image Transcription
=T.DIST.2T(8.439,39) E F 2.48178E-10 LL

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Hypothesis Testing

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