Question

Consider the hypothesis test given by

H0:μ=650Ha:μ<650

Assume the population is normally distributed. In a random sample of 25 subjects, the sample mean is found to be ´x=640, and the sample standard deviation is s=30.

(a) (1 pt) Is this test for population proportion, mean or standard deviation? What distributionshould you apply for the critical value? The t distribution should be utilized since the population standard deviation is unknown.

(b) (1 pt) Is the test a right-tailed, left-tailed or two-tailed test? The test would be left-tailed.

(c) (2 pts) Find the test statistic. (Show work and round the answer to two decimal places)T = (640-650)/ (30/5) = -10/6 = -5/3 = -1.6667

Answer 1

t = -1.633<2.06

Step 1

Here χ is the sample mean

μ is the population mean

S is the sample standard deviation

n be the sample size

The degrees of freedom γ =n-1

Step 2:-

a) we will use t- distribution test

Here sample size n = 25

the sample mean χ =640

population mean μ =650

sample standard deviation S=30

Step 3:-

b) we will use two tailed test or left tailed test

Null Hypothesis H0 : μ=650

Alternative Hypothesis Ha:μ<650

`t = (x-u)/((S)/(√(n-1) ) )`

Step 4:-

c)

`t = (640-650)/((30)/(√(25-1) ) )`

[tex]t = -1.633

Step 5 :-

Degrees of freedom:-

The degrees of freedom of t- distribution

γ = n-1 = 25-1 = 24

The table value of t are 5% level with 24 degrees of freedom For two tailed test is 2.06

Step 6:-

Since the calculated value of t < tabulated value of t, so we accepted the null hypothesis.

The data support the assumption of a population is normally distributed