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757-Mc x D International Business cou x Aplia: Student Question x com/af/servlet/quiz?quiz action takeQuiz&quiz; probG 00000036b9d1 10050000&ctx; kathleen gilliam-001 101 ueurriaa 11:00 PM Assignment Keep the Highest 17 Attempts: 1. Testing a population mean Formulating hypotheses and determining the type of test The term "El Nino" refers to the warming of the central and eastern tropical Pacific waters that occurs every 3 to 7 years and typically lasts from 9 to 12 months. The 1997-1998 El Nino, the strongest ever recorded, affected clmate patterns worldwide. Its effect, combined with an increasing trend in annual global temperatures, made 1998 the warmest year in the 20th century. suppose you are a climatologist. You conduct a hypothesis test to determine whether the global mean temperature in the current year is lower than the global mean temperature in 1998. Assume that the global mean temperature in 1998 was 14.3 degrees Celsius (the population mean). You obtain a preliminary sample of temperatures from recording stations worldwide, which yields a sample mean of R 15.1 degrees Celsius. Let u denote the global mean temperature in the current year. Formulate your null and alternative hypotheses by selecting the appropriatavalues in the blue dropdown menus that follow. The test you conduct is Continue without saving

Explanation / Answer

1. Here we have to test the hypothesis that,

H0 : mu = 14.3 Vs H1 : mu< 14.3

where mu is the population mean for global mean temperature in the current year.

14.3 is the specified population mean for global mean temperature in the year 1998.

Xbar = 15.1

Here we can conduct either z-test or t-test.

We use z-test when population standard deviation is known and

and use t-test when population standard deviation is unknown.

2. Here we have to test the hypothesis that,

H0 : mu <= 731 Vs H1 : mu > 731

Given that, Xbar = 722

sigma = 76

n = 100

Here population standard deviation is known therefore we use here one sample z-test.

Here by using central limit theorem for large n the distribution of sample mean goes to normal with mean is 731 and standard deviation is 76/sqrt(100).

Mean = 731

sd = 7.6

The test statistic is,

z = (Xbar - mu) / sd

= (722 - 731) / 7.6

= -1.18

ALpha = level of significance = 0.05

Now we have to find critical value.

Critical value we can find by using EXCEL.

syntax :

=NORMSINV(probability)

where probability = 1 - alpha

Critical value = 1.645

Reject H0 if z > 1.645

Test statistic < critical value

Fail to reject H0 at 5% level of significance.

Conclusion : The population mean may be less than or equal to 731

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