Question

The data below represents yearly car insurance premium in the US for 10 randomly selected drivers. Assuming the data is normally distributed, test the claim that the average yearly car insurance premium for a person in the US is $1,916 using a level of significance of 1%.

1905,	1940,	1939,	1952,	1931,
1937,	1920,	1913,	1928,	1934

Enter the Null Hypothesis for this test: H0:

Enter the Alternative Hypothesis for this test: H1:

What is the p-value for this hypothesis test? Round your answer to four decimal places.

What is the decision based on the given sample statistics?

Answer 1

Solution:

One sample t-test

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H₀: the average yearly car insurance premium for a person in the US is $1,916.

Alternative hypothesis: H_a: the average yearly car insurance premium for a person in the US is not $1,916.

H₀: µ = 1916 versus H_a: µ ≠ 1916

This is a two tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 1916

Xbar = 1929.9

S = 13.93995058

n = 10

df = n – 1 = 9

α = 0.01

Critical value = - 3.2498 and 3.2498

(by using t-table or excel)

t = (1929.9 – 1916)/[ 13.93995058/sqrt(10)]

t = 3.1532

P-value = 0.0117

(by using t-table)

P-value > α = 0.01

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that the average yearly car insurance premium for a person in the US is $1,916.