The world's smallest mammal is the bumblebee bat. The mean weight of 40 randomly selected bumblebee bats is 1.659 grams, with a standard deviation of 0.264 grams.

Dr. Clifford Jones claims that the mean weight of bumblebee bats is 1.7 grams. We are interested in whether it's less than he claims. Using the t-distribution technique, is there evidence that bumblebee bats weight less on average than he claims, at each of the following levels?

The degrees of freedom are df =

The test-statistic t = (positive version of t, three places after decimal) =

The calculated 't' value = 0.9822

The degrees of freedom = n-1 =40-1 =39

The calculated 't' value = 0.9822< 2.0192 at 95% level of significance with 39 degrees of freedom.

Null hypothesis is accepted at  95% level of significance.

There is  evidence that bumblebee bats weight less on average than he claims.

Step-by-step explanation:

Step:- (1)

Given the mean weight of 40 randomly selected bumblebee bats is 1.659 grams, with a standard deviation of 0.264 grams.

Given sample size 'n' = 40

mean of the sample x⁻ = 1.659 grams

Standard deviation of the sample 'S' =  0.264 grams

Dr. Clifford Jones claims that the mean weight of bumblebee bats is 1.7 grams.

Population mean 'μ' = 1.7grams

Step:-(2)

Null hypothesis: H₀:   There is  evidence that bumblebee bats weight less on average than he claims.

Alternative hypothesis : H₁ :- There is no evidence that bumblebee bats weight less on average than he claims.

The degrees of freedom γ= n-1 =40-1 =39

we will choose level of significance = 0.95 0r 0.05

Step:-(3)

The test statistic

                        t =  -0.9822

                       |t|=|-0.9822|

                      t = 0.9822

The calculated 't' value = 0.9822

The tabulated value t = 2.0192 at 95% level of significance.

The calculated 't' value = 0.9822 < 2.024 at 95% level of significance with 39 degrees of freedom.

Null hypothesis is accepted at  95% level of significance.

Conclusion:-

There is  evidence that bumblebee bats weight less on average than he claims.

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct