Question

A new chemical process has been developed for producing gasoline.  The company claims that this new process will increase the octane rating of the gasoline. Sixteen samples of the gasoline produced with the new process are selected at random and their octane reading were: 94, 93, 97, 92, 96, 94, 95, 91, 98, 95, 92, 91, 98, 95, 92, 91, 95, 96, 97, 93. If the mean octane using the existing process is 93, is the company's claim correct (use 1%)

1) In analyzing the data, what is the t score of the test statistic (study Result)?

a.

2.42

b.

2.00

c.

1.25

d.

none of the choices

2) If the decision rule is 2.53 ( the cut off on the chart) based on the information you gathered in the previous questions) would you reject the null?

	a.	none of the choices
	b.	the study result equals the decision rule so I would reject the null
	c.	yes because the study result is greater than the decision  rule
	d.	no because the study result is less than the decision rule

Answer 1

Given:

A new chemical process has been developed for producing gasoline.

The gasoline produced with the new process are selected at random and their octane reading were:

x= 94, 93, 97, 92, 96, 94, 95, 91, 98, 95, 92, 91, 98, 95, 92, 91, 95, 96, 97, 93.

Sample mean :

Σx = 1885 and n = 20

x̄ = Σx/n = 2885/20 = 94.25

Sample mean, x̄ = 94.25

Standard deviation :

Steps

= √1/20-1[(94-94.25)^2+.......+(93-94.25)^2]

= √101.75/19

√5.355

= 2.31

Standard deviation, s = 2.31

Claim : The company claims that this new process will increase the octane rating of the gasoline.

Hypothesis test:

The null and alternative hypothesis is

Ho : = 93

Ha : > 93

Since population standard deviation is unknown, we use t- test.

a) Tezt statistics :

t = x̄ - / s/√n

= 94.25 - 93/ 2.31/√20

= 2.42

The value of test statistics is t = 2.42

Answer - option A.

b) If the decision rule is 2.53.

Reject Ho if t > 2.53, otherwise fail to reject.

Since test statistics t < 2.53, we fail to reject null hypothesis.

We do not reject the null.

no because the study result is less than the decision rule

Answer - option D