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3. In a study of the relationship of the shape of a tablet to its dissolution time, 6 disk-shaped ibuprofen tablets and 8 oval-shaped ibuprofen tablets were dissolved in water. The dissolve times, in seconds, were as follows: Disk: 269.0, 249.3, 255.2, 252.7, 247.0, 261.6 Oval: 268.8, 260.0, 273.5, 253.9, 278.5, 289.4, 261.6, 280.2 Can you conclude that the mean dissolve time is less for disk shaped tablets than for mean dissolve time for oval shaped tablets? Assume that the two samples come from normal distributions and ơdisk-o,val. (a) Carry out the appropriate test at the 5% level. Be sure to show the hypothesis statements (b) Generate the appropriate 95% one-sided confidence interval.

math   Statistics-And-Probability   
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Null hypothesis: That is, the mean dissolve time is same for disk shaped tablets as for mean dissolve time for oval shaped tablets. Alternative hypothesis: That is, the mean dissolve time is less for disk shaped tablets than for mean dissolve time for oval shaped tablets. Rejection rule: If p-vaue sa(-0.05), then reject the null hypothesis Ho Excel add-in (Mega Stat) procedure: Step 1: In EXCEL, Select Add-Ins > Mega Stat > Hypothesis Tests Step 2: Choose Compare Two Independent Groups. Step 3: Choose Data Input.Step 4: In Group 1, enter the column of Disk. Step 5: In Group 2, enter the column of Oval. Step 6: Enter 0 Under Hypothesized difference. Step 7: Check t-test (pooled variance), enter Confidence level as 95.0 Step 8: Choose less than in alternative Step 9: Click OK. Excel add-in (Mega Stat) output:Hypothesis Test: Independent Groups (t-test, pooled variance) Disk Oval 255.800 270.738mean 8.216 11.903 std. dev. 8 n 12 df 14.9375 difference (Disk - Oval) 110.7749 pooled variance 10.5250 pooled std. dev. 5.6841 standard error of difference 0 hypothesized difference -2.63 t 0110 p-value (one-tailed, lower) -27.3222 confidence interval 95.% lower -25528 confidence interval 95% upper 12.3847 margin of error The p-value is 0.0110 Conclusion:Use a significance level, α 0.05 Here, p-Value is 0.0110, which is lesser than the value of α-0.05 That is, p-value(-0.0110)< α(-0.05) Therefore, by the rejection rule, reject the null hypothesis H Interpretation There is sufficient evidence at level of significance α 0.05 That is, the mean dissolve time is less for disk shaped tablets than for mean dissolve time for oval shaped tablets.From above Excel output, the 95% one-sided confidence interval is -27.3222<H 2 -2.5528

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