We first need to turn our mixed numbers into fractions by multiplying the while number by the denominator, then adding the numerator. When we do this, 5 3/6 turns into 33/6 and 2 1/3 turns into 7/3. Now we have this:

33/6-7/3

Now we need to find the Least common multiple of the denominators in order to find our common denominator, which in this case is 6. 33/6 already has a denominator of 6, so we do not need to do anything to it. To give a denominator of 6 to 7/3, however, we must multiply by 2, giving us this:

33/6-14/6

Now we can subtract the numerators.

19/6

To turn this back into a mixed number, we divide 19 by 6, which gives us 3 with a remainder of 1. Therefore, our answer is 3 1/6. This is an equivalent fraction to the fourth answer, 3 3/18.

HTH :)

4 0

3 years ago

Construct a 98% confidence interval to determine whether there is any difference between the mean drug concentration in tablets

inna [77]

Answer:

Step-by-step explanation:

So, we are given two sites;

Site one: 91.28 , 92.83, 89.35, 91.90 82.85, 94.83, 89.83, 89.00, 84.62, 86.96, 88.32, 91.17, 83.86, 89.74, 92.24, 92.59, 84.21, 89.36, 90.96, 92.85, 89.39, 89.82, 89.91, 92.16, 88.67.

=> The mean = add up all the numbers/ the total numbers (which is 25). = 89.55.

=> The standard deviation = 3.005

SITE TWO: 89.35 86.51 89.04 91.82 93.02 88.32 88.76 89.26 90.36 87.16 91.74 86.12 92.10 83.33 87.61 88.20 92.78 86.35 93.84 91.20 93.44 86.77 83.77 93.19 81.79.

=> The mean= add up all the numbers/ the total numbers (which is 25). = 89.033.

=> Standard deviation = 3.271.

NB: the assumption here is that the variance for both sites are the same.

STEP ONE: DETERMINE THE DEGREE OF FREEDOM AND THE CRITICAL VALUE.

The degree of freedom =( mean of site 1 ) + (mean of site 2) - 2 = (25 + 25) − 2 = 48.

Since the degree of freedom is 48, Recall that the value for alpha given = 0.02. Then, the critical value = 2.407.

STEP TWO: DETERMINE THE STANDARD DEVIATION AND THE STANDARD ERROR FOR BOTH.

Therefore, the standard deviation = √[( 25 - 1) × 3.005^2 + (25 -1) × 3.271^2) ÷ (25 +25 - 2) ] = 3.14.

Also, the standard error = standard deviation × ( √(1/ mean 1 + 1/mean 2) ..

Standard error = 3.14 × [ ✓( 1/25 + 1/25)] = 0.89.

STEP THREE: DETERMINE THE CONFIDENCE INTERVAL.

confidence interval = (89.548 - 89.033 - 2.41 × 0.89, 89.548 - 89.033 + 2.41 × 0.89) = (- 1.62, 2.65).

STEP FOUR: THE HYPOTHESES.

=> THE TWO TAILED TEST.

Jo:μ1 = μ2.

Ja: μ1 ≠ μ2.

Thus, the rejected region is {t : ∣ t ∣ > 2.7}

As critical value = 2.7 for the degree of freedom which is 48 and α=0.01.

If we do the t - test for this,.we will have;

(89.548 - 89.003)÷ ( standard deviation × √ ( 1/25 + 1/25). = 0.58.

So,from our t - value, is less or equals to the critical value, therefore, the null hypothesis is not rejected.

Also, from the p-value table which gives p=0.565. The p- value is greater than or equal to the alpha value(0.01). therefore, the null hypothesis is not rejected.

We are not going to reject the null hypothesis because the information gathered is not enough.

3 0

2 years ago