Question

A random sample of 11 observations taken from a population that is normally distributed produced a sample mean of 42.4 and a standard deviation of 8. Find the range for the p-value and the critical and observed values of t for each of the following tests of hypotheses using, α=0.01.

Use the t distribution table to find a range for the p-value.

Round your answers for the values of t to three decimal places.

a. H0: μ=46 versus H1: μ<46.

Enter your answer; < p-value <

tcritical	=
tobserved	=

b. H0: μ=46 versus H1: μ≠46.

Enter your answer; < p-value <

tcritical left	=
tcritical right	=
tobserved	=

Answer 1

Solution :

=46

=42.4

S = 8

n = 11

a ) This is the left tailed test .

The null and alternative hypothesis is ,

H0 :    = 46

Ha : < 46

Test statistic = t

= ( - ) / S / n

= (42.4-46) / 8 / 11

= −1.575

Test statistic = t =−1.575  

critical t value =−2.764.

to observed that t =−1.575 ≥ tc​ =−2.764

P-value =0.0731

= 0.01

P-value <

0.0731 > 0.01

Faail to reject the null hypothesis .

There is not sufficient evidence to claim that the population mean μ is less than 46, at the 0.01 significance level.

b ) This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 46

Ha :     46

Test statistic = t

= ( - ) / S / n

= (42.4-46) / 8 / 11

= −1.575

Test statistic = t =−1.575

critical t value = 3.169

to observed that ∣t∣=1.575 ≤ tc​ =3.169

P-value =0.1462

= 0.01

P-value <

0.1462 > 0.01

Faail to reject the null hypothesis .

There is not sufficient evidence to claim that the population mean μ is different than 46, at the 0.01 significance level.