The manager of a mall conducted a survey among two groups (n1 = 100, n2 = 100) of visitors to the mall on different days. She found that the first group spent an average of 60 minutes in the mall, while the second group spent an average of 90 minutes in the mall.If the manager wishes to see the difference in the average times spent by the two groups in the mall, which of the following sets shows the null hypothesis and alternative hypothesis?Null Hypothesis: There is at least some difference in the average times spent by the two groups in the mall.Alternative Hypothesis: The difference in the average times spent by the two groups in the mall is 30 minutes.Null Hypothesis: There is no difference in the average times spent by the two groups in the mall.Alternative Hypothesis: There is at least some difference in the average times spent by the two groups in the mall.Null Hypothesis: There is at least some difference in the average times spent by the two groups in the mall.Alternative Hypothesis: There is no difference in the average times spent by the two groups in the mall.Null Hypothesis: There is no difference in the average times spent by the two groups in the mall.Alternative Hypothesis: There is a difference in the average times spent by the two groups in the mall, with a standard deviation of 30 minutes.
Question
The manager of a mall conducted a survey among two groups (n1 = 100, n2 = 100) of visitors to the mall on different days. She found that the first group spent an average of 60 minutes in the mall, while the second group spent an average of 90 minutes in the mall.If the manager wishes to see the difference in the average times spent by the two groups in the mall, which of the following sets shows the null hypothesis and alternative hypothesis?Null Hypothesis: There is at least some difference in the average times spent by the two groups in the mall.Alternative Hypothesis: The difference in the average times spent by the two groups in the mall is 30 minutes.Null Hypothesis: There is no difference in the average times spent by the two groups in the mall.Alternative Hypothesis: There is at least some difference in the average times spent by the two groups in the mall.Null Hypothesis: There is at least some difference in the average times spent by the two groups in the mall.Alternative Hypothesis: There is no difference in the average times spent by the two groups in the mall.Null Hypothesis: There is no difference in the average times spent by the two groups in the mall.Alternative Hypothesis: There is a difference in the average times spent by the two groups in the mall, with a standard deviation of 30 minutes.
Solution
The correct set of hypotheses for this scenario would be:
Null Hypothesis: There is no difference in the average times spent by the two groups in the mall.
Alternative Hypothesis: There is at least some difference in the average times spent by the two groups in the mall.
In hypothesis testing, the null hypothesis typically represents a theory that has been put forward, either because it is believed to be true or because it is to be used as a basis for argument, but has not been proved. In this case, the null hypothesis is that there is no difference in the average times spent by the two groups in the mall.
The alternative hypothesis, on the other hand, is a statement that is accepted if the null hypothesis is rejected. In this case, the alternative hypothesis is that there is at least some difference in the average times spent by the two groups in the mall.
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