Question

Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).† Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows.

3.7

2.9

3.8

4.2

4.8

3.1

The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and σ = 0.74 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.55 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.55 grams? Use α = 0.01.

(a)Compute the z value of the sample test statistic. (Round your answer to two decimal places.)

(b) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Answer 1

Null hypothesis

                   
                      
Alternative hypothesis       

               
                      
We have given,                      
Population mean for given example =4.55              
Sample mean=3.75              
Population standard deviation =   0.74              
Sample size for given example =   6              
Level of significance =   0.01              
Z test statistic formula

(b) P value is =0.0040....................by using Z table or by using Excel command NORMSDIST(-2.65)