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In: Statistics and Probability

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final...

Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.
Various temperature measurements are recorded at different times for a particular city. The mean of 20°C is obtained for 60 temperatures on 60 different days. Assuming that test the claim that the population mean is 22°C . Use a 0.05 significance level. Testing Hypothesis Z-Table

Solutions

Expert Solution

Null Hypothesis H0: = 22

Altenative Hypothesis Ha: 22

Sample mean,   = 20

Population Standard deviation = 1.5

Since we know the true population standard deviation we will conduct one sample z test.

Standard error of mean, SE = /  = 1.5 / = 0.1936492

Test statistic, z = ( - ) / SE =  (20 - 22) / 0.1936492 = -10.328

For two-tail test, p-value = 2 * p(z < -10.328) =  0.0000

Since, p-value is less than 0.05 significance level, we reject null hypothesis H0.

We conclude that there is significant evidence from the sample data that true mean temperature of the city is different from 22 degree Celsius.

orchestra answered 1 year ago
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