Answer to Question #230765 in Statistics and Probability for hiz

Question

In a study, the effect of adding nitroglycerin to different polymers on the melting temperatures of polymers is investigated. For this purpose, melting temperatures were determined by adding the same amount of nitroglycerin to 5 different polymers. Test whether the melting temperatures change at the 5% significance level.

Polimer adı

A260

B12C

B244

A006

C66D

Nitrogliserin öncesi erime sıcaklığı (⁰C)

302

268

294

282

306

Nitrogliserin sonrası erime sıcaklığı (⁰C)

307

295

291

294

308

Answer 1

Using R

$H_0: \mu_1=\mu_2 \\ H_1: \mu_1≠\mu_2$

With paired data we are interested in the difference between each paired value.

Our test for normality should be conducted on the single sample distribution represented by the difference between before and after (the variable diff). Let’s test date for normality using shapiro.test().

The samples appear to be normally distributed so we may proceed with a standard t-test.

Since $P_{cal}=0.1736 > P = 0.05$

Accept H₀.

There is enough evidence to conclude that the melting temperatures did NOT change at the 5% significance level.