Question

An engineer wants to know if producing metal bars using a new experimental treatment rather than the conventional treatment makes a difference in the tensile strength of the bars​ (the ability to resist tearing when pulled​ lengthwise). At alphaαequals=0.020 answer parts​ (a) through​ (e). Assume the population variances are equal and the samples are random. If​ convenient, use technology to solve the problem.

Experimental Treatment   Conventional Treatment
420   387
350   432
422   437
355   360
425   358
360   435
448   412
415
355
364

​(a) Identify the claim and state

Upper H 0H0

and

Upper H Subscript aHa.

The claim is​ "The new treatment

▼

makes a difference

does not make a difference

in the tensile strength of the​ bars."What are

Upper H 0H0

and

Upper H Subscript aHa​?

The null​ hypothesis,

Upper H 0H0​,

is

▼

mu 1 equals mu 2μ1=μ2

mu 1 less than or equals mu 2μ1≤μ2

mu 1 greater than or equals mu 2μ1≥μ2

. The alternative​ hypothesis,

Upper H Subscript aHa​,

is

▼

mu 1 not equals mu 2μ1≠μ2

mu 1 greater than mu 2μ1>μ2

mu 1 less than mu 2μ1<μ2

.

Which hypothesis is the​ claim?

The alternative​ hypothesis, Upper H Subscript aHa

The null​ hypothesis, Upper H 0H0

​(b) Find the critical​ value(s) and identify the rejection​ region(s).

Enter the critical​ value(s) below.

nothing

​(Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as​ needed.)

Select the correct rejection​ region(s) below.

A.

t less than minus t 0 comma t greater than t 0t<−t0, t>t0

B.

negative t 0 less than t less than t 0−t0<t<t0

C.

t greater than t 0t>t0

D.

t less than minus t 0t<−t0

​(c) Find the standardized test statistic.

tequals=nothing

​(Type an integer or decimal rounded to the nearest thousandth as​ needed.)

​(d) Decide whether to reject or fail to reject the null hypothesis.

▼

Fail to reject

Reject

the null hypothesis.

​(e) Interpret the decision in the context of the original claim.

At the

2 %2%

significance​ level,

▼

there is not

there is

enough evidence to support the claim.

Click to select your answer(s).

Answer 1

= 391.4, s1^2 = 1416.044, n1 = 10

= 403, s2^2 = 1205.33, n2 = 7

The new treatment makes a difference in the tensile strength of the bars.

H₀:

H₁:

The claim is the alternative hypothesis H_a.

b) df = 10 + 7 - 2 = 15

At = 0.02, the critical values are t_{0.01, 15} = +/- 2.602

Reject H₀, if t < -2.602 or t > 2.602

c) The pooled variance(s_p²) = ((n1 - 1)s1^2 + (n2 - 1)s2^2)/(n1 + n2 - 2)

                                             = (9 * 1416.044 + 6 * 1205.33)/(10 + 7 - 2)

                                             = 1331.7584

The test statistic t = ()/sqrt(s_p²/n1 + s_p²/n2)

                             = (391.4 - 403)/sqrt(1331.7584/10 + 1331.7584/7)

                             = -0.645

d) Since the test statistic value is not less than the negative critical value(-0.645 > -2.602), so we should not reject the null hypothesis.

Fail to reject the null hypothesis.

e) At the 2% significance level there is not enough evidence to support the claim.