Question

An article presents benzene conversions (in mole percent) for 24 different benzene hydroxylation reactions. The results are 52.3 41.1 28.8 67.8 78.6 72.3 9 19.0 30.3 41.0 63.0 80.8 26.8 37.3 38.1 33.6 14.3 30.1 33.4 36.2 34.6 40.0 81.2 59.4 Can you conclude that the mean conversion is greater than 30? Compute the appropriate test statistic and find the P-value. The appropriate test statistic and the P-value are and , respectively. Round the test statistic to two decimal places and the P-value to four decimal places. We (Click to select) conclude that the mean conversion is greater than 30.]

Answer 1

Test statistic = 3.21;

Pvalue = 0.0019;

Reject H0 and conclude that the mean conversion rate is greater than 30.

Explanation:

Hypothesis :

NULL ; H0 : μ = 30

ALTERNATIVE ; H0 : μ > 30

Sample, x : 52.3 41.1 28.8 67.8 78.6 72.3 9 19.0 30.3 41.0 63.0 80.8 26.8 37.3 38.1 33.6 14.3 30.1 33.4 36.2 34.6 40.0 81.2 59.4

Sample Mean, xbar = 43.71 (using calculator)

Sample standard deviation, s = 20.95 ( calculator)

Sample size, n = 24

Take, α = 0.05

Test statistic :

(xbar - μ) ÷ (s/√n)

(43.71 - 30) ÷ (20.95/√24)

13.71 / 4.2764008

Test statistic = 3.21

Degree of freedom, df = n - 1 = 24 - 1 = 23

The Pvalue, using a Pvalue calculator : (3.21, 23)

Pvalue = 0.001942

Pvalue = 0.0019 ( 4 decimal places).

Decison :

Reject H0 ; if Pvalue ≤ α

Since Pvalue is very low and lesser than α ` We reject H0 and conclude that the mean conversion rate is greater than 30.