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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

Researchers at a National Weather Center in the north-eastern United States recorded the number of 90° days each year since records first started in 1875. The numbers form a normal shaped distribution with a mean of μ = .9.6 and a standard deviation of σ = 1.9. To see if the data showed any evidence of global warming, they also computed the mean number of 90° days for the most recent n = 4 years and obtained M = 11.85. Do the data indicate that the past four years have had significantly more 90° days than would be expected for a random sample from this population? Use a one-tailed test with α = .05.

To determine
Whether the past four years have had significantly more 90° days than would be expected for a random sample from the population.

Explanation

Given info:

Samples mean (M) is 11.85, population mean is 9.6, standard deviation is 1.9, alpha level is 0.05 and sample size is 4.

Calculation:

The null hypothesis states that there is no effect of the treatment and alternative hypothesis states opposite of null hypothesis. As given in the question that population mean is 9.6 and one tailed test is used, so the null hypothesis and alternative hypothesis for this question are:

H0:μ9.6H1:μ>9.6

The alpha level is given in the question as 0.05 and need to find boundaries of the critical region. As given in the question that one tailed hypothesis test used, so the z-score critical value at α=0.05 is 1.65 using the z table. The z-score from given data is calculated as:

z=MμσM

Where σM is known as standard error and calculated as

σM=σ

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