Question

In 2019, the average weight of baby quails was 110 grams. Pollution levels in Quails natural habit has increased and a conservation group wants to know if the average weight of baby quails has reduced. A sample of 49 baby quails yielded a sample mean of 108 grams. Historical data shows that the population standard deviation is 10 grams.

At the 5% level of significance, can the conservation group conclude that baby quails have become lighter?

Would your answer change at a 1% level of significance? Justify.

Answer 1

Solution :

= 110

=108

=10

n = 49

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 110

H_a : > 110

Test statistic = z

= ( - ) / / n

= (108-110) / 10 / 49

= -1.4

P(z >-1.4 ) = 1 - P(z < -1.4 ) =1- 0.0808=0.9192

P-value = 0.9192

= 0.05  

the null hypothesis is not rejected.

P-value >

Reject the null hypothesis .

There is sufficient evidence to suggest that   

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean \muμ is greater than 110, at the 0.05 significance level

(b)

1% level of significance Justify.

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean \muμ is greater than 110, at the 0.01 significance level