An experiment was planned to compare the mean time (in days) required to recover from a common cold for persons given a daily dose of 4 mg of vitamin C versus those who were not given a vitamin C supplement. Suppose that 35 adults were randomly selected for each treatment category. For the group taking vitamin C the mean recovery time was 5.8 days with a standard deviation of 1.2 days. For the group not taking vitamin C the mean recovery time was 6.9 days with a standard deviation of 2.9 days. Do the data present sufficient evidence vitamin C reduces the mean time required to recover from a common cold? Test using α = 2.5%. a. State the Null Hypothesis H0 : b. State the Alternative Hypothesis Ha : c. Draw a curve listing the Null Region, Alternative Region (with area), and critical value(s). d. Calculate the test statistic. e. State your conclusion.
Added by David V.
Step 1
State the Null Hypothesis H0: The null hypothesis is that there is no difference in the mean recovery time between the two groups. In other words, the mean recovery time for the group taking vitamin C (μ1) is equal to the mean recovery time for the group not Show more…
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An experiment was planned to compare the mean time (in days) to recover from a common cold for people given a daily dose of 4 milligrams (mg) of vitamin C versus those who were not. Suppose that 35 adults were randomly selected for each treatment category and that the mean recovery times and standard deviations for the two groups were as follows: $$ \begin{array}{lcc} \hline & \begin{array}{l} \text { No Vitamin } \\ \text { Supplement } \end{array} & \begin{array}{c} 4 \mathrm{mg} \\ \text { Vitamin C } \end{array} \\ \hline \text { Sample Size } & 35 & 35 \\ \text { Sample Mean } & 6.9 & 5.8 \\ \text { Sample Standard Deviation } & 2.9 & 1.2 \end{array} $$ a. If you want to show that the use of vitamin $\mathrm{C}$ reduces the mean time to recover from a common cold, give the null and alternative hypotheses for the test. Is this a one- or a two-tailed test? b. Conduct the statistical test of the null hypothesis in part a and state your conclusion. Test using $\alpha=.05$
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Perform each of the following steps. a. State the hypotheses and identify the claim. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results. Use the traditional method of hypothesis testing unless otherwise specified. The average length of "short hospital stays" for men is slightly longer than that for women, 5.2 days versus 4.5 days. A random sample of recent hospital stays for both men and women revealed the following. At $\alpha=0.01$, is there sufficient evidence to conclude that the average hospital stay for men is longer than the average hospital stay for women? $$ \begin{array}{lll} & \text { Men } & \text { Women } \\ \hline \text { Sample size } & 32 & 30 \\ \text { Sample mean } & 5.5 \text { days } & 4.2 \text { days } \\ \text { Population standard deviation } & 1.2 \text { days } & 1.5 \text { days } \end{array} $$
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