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

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

Step 4:-

c)

[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

$3720

step-by-step explanation:

taxable income = $31000

as per the 2018-2019 us tax bracket, the tax rate is 12% for an individual whose taxable income is between $9,526 to $38,700.

so, the tax to be paid by him = 12% of 31000

= 0.12 * 31000     [12% converted to decimal as 0.12]

= $3720