The difference of sample means of two populations is 108.7, and the standard deviation of the difference in sample means is 32. Which statement is true if we are testing the null hypothesis at the 68% confidence level?

AThe difference of the two means is significant at the 68% confidence level, so the null hypothesis must be rejected.

BThe difference of the two means is significant at the 68% confidence level, so the null hypothesis must be accepted.

CThe difference of the two means is not significant at the 68% confidence level, so the null hypothesis must be rejected.

DThe difference of the two means is not significant at the 68% confidence level, so the null hypothesis must be accepted.

'The null hypothesis is a typical statistical theory which suggests that no statistical relationship and significance exists in a set of given single observed variable, between two sets of observed data and measured phenomena.'

According to the given problem,

Mean = 108.7

Standard Deviation = 32

We know,

z-score = \(\frac{mean}{Standard Deviation}\)

= \(\frac{108.7}{32}\)

= 3.396

≈ 3.4

Therefore, the confidence level of 68% is equivalent to a z-score of 1.

Also, the sample z-score is far beyond that of the confidence interval.

Hence, we can conclude, the difference of the two means is significant at the 68% confidence level, so the null hypothesis must be rejected.

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