Question

A proposed null hypothesis states that there is no difference in the population mean heights of two neighboring districts. The difference of the sample means is 10 cm, and the standard deviation of the difference of sample means is 6 cm. Which conclusion can we draw at the 68% confidence level?
A. The population means of the two districts are different.

B. The population means of the two districts are not different.

C. The difference of the sample means of the two districts is 0.

D. The sample means of the two districts are not different.

Answer 1

A. The population means of the two districts are different

State your hypotheses first Null Hypothesis 

Ho: Difference in Population means = 0 

Alternate Hypothesis Ha: Difference in population means is not equal to zero. 

The alternate hypothesis implies we need a two tailed hypothesis test. The empirical rule says that 68% of normally distributed data is within 1 standard deviation of the mean. 

This is also known as the 68-95-99.7 rule. The 68% confidence level gives us the 'fail to reject null hypothesis" region of (-1, 1). But if the test statistic falls outside this interval, we reject the null hypothesis. 

The test statistic z score is z = 10 / ( 6) = 1.67 since your test statistic falls outside the confidence level, we reject the null Hypothesis that there is no difference in the means. So there is evidence to suggest that there is a significant difference in the means.

Answer 2

Answer:

Option A is correct answer.

A. The population means of the two districts are different.

Explanation:

Null hypothesis is something that states that there is no difference between the population means, while the alternative hypothesis states that there is difference between the two.

So, If the difference of the sample means is 10cm, and the standard deviation of the difference of sample means is 6 cm. Then  the population means of the two districts will be different according to the manual solution.