Question

Two populations have mound-shaped, symmetric distributions. A random sample of 16 measurements from the first population had a sample mean of 20, with sample standard deviation 2. An independent random sample of 9 measurements from the second population had a sample mean of 19, with sample standard deviation 3. Test the claim that the population mean of the first population exceeds that of the second. Use a 5% level of significance.

a) What distribution does the sample test statistic follow? Explain.

b) State the hypothesis.

c) Compute ?̅1 − ?̅2 and the corresponding sample distribution value.

d) Estimate the P-value of the sample test statistic.

e) Conclude the test.

f) Interpret the results.

Answer 1

Answer:

a)

As we are given here the example standard deviations, the t-appropriation would be utilized to do the theory testing.

b)

As we need to here test the case that the populace mean of the main populace surpasses that of the second,

Null hypothesis

Alternative hypothesis  

c)

The point gauge of the distinction in methods is registered as:

X1bar - X2bar = 20 - 19

= 18

The test statistics is given as follows

t = (X1bar - X2bar) / sqrt ((s1^2/n1) + (s2^2/n2))

substitute values

t = 1/(sqrt((2^2/16) + (3^2/9))

t = 0.8944

Consequently 0.8944 is the esteem of the test measurement here.

d)

The p-value for this one followed test here is processed as:

p = P (t {n1 + n2 - 2} > 0.8944)

p = P (t {23} > 0.8944) = 0.1902

e)

Here p-value is 0.1902 > 0.05 that is the alpha i.e., level of sigificance, the test is insignificant here and we can't reject the Ho (null hypothesis)

f)

Here we can't reject the null hypothesis Ho i.e., we dont have enough proof to claim that the populace mean of the main populace surpasses that of the second