Question

At α = 10, test to see if the mean of the distribution from which this data came is 2500 or is it higher? Assume the data is from a Normal Distribution.

2570 2593 2787 2510 2563

2383 2507 2601 2520 2468

A. give the null and alternative hypotheses

B Give the critical values of the test

C. Give the test statistic

D. Give the p value

E. Give the type of error you could have made

Answer 1

A. give the null and alternative hypotheses

Null hypothesis: H₀: The mean of the distribution from which data came is 2500.

Alternative hypothesis: H_a: The mean of the distribution from which data came is greater than 2500.

H₀: µ = 2500 versus H_a: µ > 2500

This is an upper tailed test.

B Give the critical values of the test

We are given

Level of significance = α = 0.10

n = 10

df = n – 1 = 9

Critical value = 1.3830

(by using t-table)

C. Give the test statistic

Test statistic = t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

Xbar = 2550.2

S = 105.488072

n = 10

t = (2550.2 – 2500)/[ 105.488072/sqrt(10)]

t = 1.5049

Test statistic = t = 1.5049

D. Give the p value

P-value = 0.0833

(by using t-table)

P-value < α = 0.10

So, we reject the null hypothesis

There is sufficient evidence to conclude that the mean of the distribution from which data came is greater than 2500.

E. Give the type of error you could have made

There would be a type I error because we reject the null hypothesis for the above test.