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Surname 1

Student’s Name

Instructor’s Name

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Date

Statistical Questions

Hypothesis;

H0: The bumblebee bats come from the same population and have a mean weight of =1.8g

H1: The bumblebee bats do not come from the same population and have a mean weight of  ≠ 1.8g

T-statistics

Standard score, z=









=











=





=1.7133

S=0.508676

Z= 





Z=0.66012

P(X=1.8) = P(Z=0.66012) = 1.36

Surname 2

α/2

=1.96

P(X=1.8) = P(Z=0.66012) = 1.36

α/2

=1.96

Since p(x=0.66012 < Z

α/2

, do not reject H0 and conclude that the bumblebee bats come from the

same population and have a mean weight of =1.8g.

The confidence interval of the proportion of the bumblebee bats that come from the same

population with a mean weight of =1.8g is constructed as follows;

The confidence interval is computed based on the mean and standard deviation of the sampling

distribution of a proportion. The formulas for these two parameters are shown below:

μp = π

Since we do not know the population parameter π, we use the sample proportion p as an

estimate. The estimated standard error of p is therefore

is calculated as shown below:



  =0.12908

To correct for the fact that we are approximating a discrete distribution with a continuous

distribution (the normal distribution), we subtract 0.5/N from the lower limit and add 0.5/N to the

upper limit of the interval. Therefore, the confidence interval is

Surname 3

Lower limit: 0.66012 - (1.96)(0.12908) – 0.03333 = 0.3737932

Upper limit: 0.66012 + (1.96)(0.12908) + 0.03333 = 0.9464468

Thus the confidence interval is 0.3737932≤π≤0.9464468

In terms of percent, between 37.37932% and 94.64468 of the bumblebee bats come from the

same population and have a mean weight of =1.8g.

The confidence interval provides a good estimate of the population proportion since it has a

small margin of error.

2. The independent t-test and confidence interval are parametric methods appropriate for

examining the difference in means for two populations. They can also be thought of a way of

examining the relationship between a numeric outcome of why variables and a categorical

explanatory or x variables.

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