Researchers studied whether hormone levels tend to differ following days of strenuous activity as opposed to days of no strenuous activity. For each of six subjects, one blood sample was taken after a day in which the person engaged in strenuous exercise, and one blood sample was taken after a day that included no strenuous activity. The data on growth hormone levels (in $\mathrm{mg} / \mathrm{ml}$ ) follow, along with some summary statistics:
a. Is a paired $t$-test or an independent-samples $t$-test appropriate here? Explain briefly.
b. State the appropriate hypotheses, in words as well as in symbols.
c. Calculate the test statistic, and determine the $p$-value as accurately as possible.
d. Using the $\alpha=.05$ significance level, summarize the conclusion you would draw about this study. (Be sure to relate your conclusion to the context.)
e. If the sample size were larger, and all else remained the same, would these results produce stronger, weaker, or the same level of evidence that hormone levels differ after strenuous activity? (No explanation is needed.)

Question

Researchers studied whether hormone levels tend to differ following days of strenuous activity as opposed to days of no strenuous activity. For each of six subjects, one blood sample was taken after a day in which the person engaged in strenuous exercise, and one blood sample was taken after a day that included no strenuous activity. The data on growth hormone levels (in $\mathrm{mg} / \mathrm{ml}$ ) follow, along with some summary statistics:  
a. Is a paired $t$-test or an independent-samples $t$-test appropriate here? Explain briefly.
b. State the appropriate hypotheses, in words as well as in symbols.
c. Calculate the test statistic, and determine the $p$-value as accurately as possible.
d. Using the $\alpha=.05$ significance level, summarize the conclusion you would draw about this study. (Be sure to relate your conclusion to the context.)
e. If the sample size were larger, and all else remained the same, would these results produce stronger, weaker, or the same level of evidence that hormone levels differ after strenuous activity? (No explanation is needed.)

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The Answer of Researchers studied whether hormone levels tend to differ following days of strenuous activity as opposed to days of no strenuous activity. For each of six subjects, one blood sample was taken after a day in which the person engaged in strenuous exercise, and one blood sample was taken after a day that included no strenuous activity. The data on growth hormone levels (in $\mathrm{mg} / \mathrm{ml}$ ) follow, along with some summary statistics:  
a. Is a paired $t$-test or an independent-samples $t$-test appropriate here? Explain briefly.
b. State the appropriate hypotheses, in words as well as in symbols.
c. Calculate the test statistic, and determine the $p$-value as accurately as possible.
d. Using the $\alpha=.05$ significance level, summarize the conclusion you would draw about this study. (Be sure to relate your conclusion to the context.)
e. If the sample size were larger, and all else remained the same, would these results produce stronger, weaker, or the same level of evidence that hormone levels differ after strenuous activity? (No explanation is needed.)

Researchers Studied Whether Hormone Levels Tend to Differ Following Days mg/ml\mathrm{mg} / \mathrm{ml}mg/ml

Researchers Studied Whether Hormone Levels Tend to Differ Following Days $\mathrm{mg} / \mathrm{ml}$