Question

Tensile-strength tests were carried out on two different grades of wire rod. Grade 1 has 10 observations yielding a sample mean of 1085 and standard deviation of 52. Grade 2 has 15 observations yielding a sample mean of 1034 and standard deviation of 61. Assume the populations to be approximately normal with equal variances.

State and conclude your hypothesis at the 0.05 level of significance if grade 1 and grade 2 true means are equal each other?

Find P-Value.

Answer 1

solution:

the provided information are as follows:

for grade 1:

for grade 2:

the null and alternative hypothesis:

This corresponds to a two-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.

Rejection region:

degree of freedom = df =

critical value of t =

The rejection region for this two-tailed test is

test statistics:

where pooled variance =

p value at 23 df, and t = 2.167 = 0.0408

since p value = 0.0408 < 0.05, so rejecting the null hypothesis

conclusion:

there is enough evidence to conclude that the true mean of grade one is different from the true mean of grade 2.