True or False 1 Researchers measured the bone minreral densi

True or False

1. Researchers measured the bone minreral density of 94 women and calculated the 95% CI for hte mean as (0.984, 1.048). Then the 95% CI would mean that 95% of the sampled bone mineral density measurements are between 0.984 abd 1.048

2. As the size of the two samples increase given the variable standard deviations are kept the same, then the width of the 95% CI for (u1-u2) will also increase.

3. A researcher conducted a hypothesis test to see if students on average perform better on exams given in the morning than exams given in the afternoon. The P value based on an appropriate test procedure is 0.01. This means that it is rare to observe current test statsistics value given the H0 is true. As a result, we successfully reject the null hypothesis at a=0.05

4. Suppose that sa study is conducted using a paired desing, but theat the pairing is ignored in the analysis of the data. The width of confidence interval would be smaller than paired-sample confidence interval at same level confidence.

Solution

1. FALSE. This is a confidence interval for the mean, not the measurements.

Researchers measured the bone minreral density of 94 women and calculated the 95% CI for hte mean as (0.984, 1.048). Then the 95% CI would mean that 95% of the sampled bone mineral density measurements are between 0.984 abd 1.048
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2. FALSE. The width decreases becasue the standard error decreases with increasing sample size.

As the size of the two samples increase given the variable standard deviations are kept the same, then the width of the 95% CI for (u1-u2) will also increase.

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3. TRUE.

A researcher conducted a hypothesis test to see if students on average perform better on exams given in the morning than exams given in the afternoon. The P value based on an appropriate test procedure is 0.01. This means that it is rare to observe current test statsistics value given the H0 is true. As a result, we successfully reject the null hypothesis at a=0.05

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4. FALSE. The paired confidence interval would be narrower, as it would have lesser standard error.

Suppose that sa study is conducted using a paired desing, but theat the pairing is ignored in the analysis of the data. The width of confidence interval would be smaller than paired-sample confidence interval at same level confidence.