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 a standard deviation of 52. Grade 2 has 15 observations yielding a sample mean of 1034 and a 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 to each other.

We see that the p value is lower than the significance level provided of 0.05 so then we have enough evidence to conclude that the true means are different at 5% of significance.

Step-by-step explanation:

Data given

represent the sample size for group 1

represent the sample size for group 2

represent the sample mean for the group 1

represent the sample mean for the group 2

represent the sample standard deviation for group 1

represent the sample standard deviation for group 2

We are assuming that the two samples are normally distributed with equal variances and that means:

System of hypothesis

Null hypothesis:

Alternative hypothesis:

The statistic is given by:

The degrees of freedom are given by:

And the pooled variance is:

Replacing we got:

And the deviation would be:

The degrees of freedom are:

The statistic would be:

The p value would be

We see that the p value is lower than the significance level provided of 0.05 so then we have enough evidence to conclude that the true means are different at 5% of significance.