In a study of the relationships 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 σdisk= σoval.

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.

Step-by-step explanation:

Hello!

a.

The objective is to study the relationship between the shape of an ibuprofen tablet and its dissolution time.

For these two independent samples of tablets from different shapes where taken and their dissolution times measured:

Sample 1: Disk.shaped tablets

n₁= 6

X[bar]₁= 255.8

S₁= 8.22

Sample 2: Oval-shaped tablets

n₂=8

X[bar]₂= 270.74

S₂= 11.90

Assuming that the population variances are equal and both samples come from normal distributions you need to test if the average dissolution time of the disk-shaped tablets is less than the average dissolution time of the oval-shaped tablets, symbolically:

H₀: μ₁ ≥ μ₂

H₁: μ₁ < μ₂

α: 0.05

Considering the given information about both populations, the statistic to use for this test is a Student t for independent samples with pooled sample variance:

Sa²= 110.76

Sa= 10.52

This test is one-tailed to the left, meaning that you will reject the null hypothesis to small values of t, the p-value has the same direction and you can calculate it as:

P(t₁₂≤-2.63)= 0.0110

Since the p-value= 0.0110 is less than the significance level α: 0.05, the decision is to reject the null hypothesis.

At a 5% significance level you can conclude that the average dissolution time of the disk-shaped ibuprofen tablets is less than the average dissolution time of the oval-shaped ibuprofen tablets.

b.

(X[bar]₁-X[bar]₂)+Sa

(255.8-270.74)+ 10.52*

(-∞;-4.815)

I hope it helps!

its 69.420

step-by-step explanation: