Question

The melting point of 16 samples of a brand of olive oil was determined and the sample mean came out to be 95.52. Assume that the distribution of the melting point is normal with a standard deviation of 1.5. Test H0: μ=95 against Ha: μ̸ is not equal to 95 at the 10% significance level. Do the problem by first obtaining the rejection region and second, by using the p-value.

Answer 1

H₀ : = 95

H_a: 95

significance level = 0.10

sample mean = = 95.52

sample size =n = 16

Population standard deviation = = 1.5

standard error = /sqrt(n) = 1.5/sqrt(16) = 0.375

Rejection Region method :

Here as significance level is 0.10 and test is two tailed.

So, Critical value = Z_critical = +-1.645

so, we will reject the null hypothesis when Z < -1.645 or Z > 1.645

so here test statistic

Z = (95.52 - 95)/0.375 = 1.3867

so here Z < Z_critical so we would fail to reject the null hypothesis and conclude that melting point is equal to 95^o C.

p - value method :

here p - value = 2 * P(Z > 1.3867) = 2 * [1 - NORMSDIST(1.3867)] = 2 * 0.08277 = 0.1655

Here p value is greater than 0.10 so we would fail to reject the null hypothesis and conclude that melting point is equal to 95^o C.