Question

You wish to test the following claim (HaHa) at a significance level of α=0.01α=0.01.      

Ho:μ=59.9Ho:μ=59.9
Ha:μ<59.9Ha:μ<59.9

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=18n=18 with mean ¯x=56.3x¯=56.3 and a standard deviation of s=19.3s=19.3.

1. What is the test statistic for this sample?
   
   test statistic =  Round to 3 decimal places
   
2. What is the p-value for this sample?
   
   p-value =  Use Technology Round to 4 decimal places.
   
3. The p-value is...
   • less than (or equal to) αα
   • greater than αα
   
   
4. This test statistic leads to a decision to...
   • reject the null
   • accept the null
   • fail to reject the null
   
   
5. As such, the final conclusion is that...
   • There is sufficient evidence to warrant rejection of the claim that the population mean is less than 59.9.
   • There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 59.9.
   • The sample data support the claim that the population mean is less than 59.9.
   • There is not sufficient sample evidence to support the claim that the population mean is less than 59.9.

Answer 1

Solution :

Given that ,

= 59.9

= 56.3

s = 19.3

n = 18

The null and alternative hypothesis is ,

H0 :   = 59.9

Ha : < 59.9

This is the left tailed test .

Test statistic = T

= ( - ) / s / n

= ( 56.3 - 59.9 ) / 19.3 / 18

= -0.791

The test statistic = -0.791

df = n - 1 = 18 - 1 = 17

P-value = 0.2199

= 0.01

0.2199 > 0.01

The p - value is greater than α

P-value >

Fail to reject the null hypothesis .

conclusion : -There is not sufficient sample evidence to support the claim that the population mean is less than 59.9.