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DIA [1.3K]
3 years ago
7

Can you conclude with a high degree of confidence that the population means for Iowa and New Jersey students are​ different? A.

Because of the extremely low p​-value, we cannot reject the null hypothesis with a very high degree of confidence.​ Hence, the population means for Iowa and New Jersey students are not different. B. Because of the extremely high p​-value, we can reject the null hypothesis with a very high degree of confidence.​ Hence, the population means for Iowa and New Jersey students are different. C. Because of the extremely low p​-value, we can reject the null hypothesis with a very high degree of confidence.​ Hence, the population means for Iowa and New Jersey students are different. D. Because of the extremely high p​-value, we cannot reject the null hypothesis with a very high degree of confidence.​ Hence, the population means for Iowa and New Jersey students are not different.

Mathematics
1 answer:
Katen [24]3 years ago
6 0

Complete Question

The complete question is  shown on the first uploaded image

Answer:

Option A is correct

Step-by-step explanation:

From the question we are told that  

  The  95% confidence interval of the mean  score of all  New Jersey third graders  is  (58.957 ,  63.043)

   The sample size is  n =  184

   The sample average is  \mu = 65 \ points

   The standard deviation is   \sigma  =  13 \ points

    The  90%  confidence interval for the difference in mean score between lowa and New Jersey is  (-6.33 ,  -1.67 )

   The  p-value is  p-value  =  0.0048

Generally given that the p-values is very low compared to the level of significance (100 -90 =  10% = 0.10 )  we can reject the null hypothesis which is usually a  claim that the means of the  population are the same )

Hence the population means are different .

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Answer:

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The z- score of the sample mean is 0.0959

(B) Is this sample significantly different from the population?

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Step -by- step explanation:

(A) To find the z- score of the sample mean,

X = 75 which is the raw score

¶ = 74 which is the population mean

S. D. = 10.43 which is the population standard deviation of/from the mean

Z = [X-¶] ÷ S. D.

Z = [75-74] ÷ 10.43 = 0.0959

Hence, the sample raw score of 75 is only 0.0959 standard deviations from the population mean. [This is close to the population mean value].

(B) To test for whether this sample is significantly different from the population, use the One Sample T- test. This parametric test compares the sample mean to the given population mean.

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Alternative hypothesis: Sample is significantly different from population

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