Question

In: Statistics and Probability

In 1898, Hermon Bumpus studied a number of house sparrows that were brought to the Anatomical...

In 1898, Hermon Bumpus studied a number of house sparrows that were brought to the Anatomical Laboratory of Brown University after an uncommonly severe winter storm. 35 birds survived and 24 perished.
In the spreadsheet, the weights of birds in grams (g) are given.
Is there a significant difference between the weights of the sparrows that perished and the weights of the sparrows that survived?
Using a t-test of independent samples (let alpha = 0.05), answer the following.

t = ? df = ?

Critical value of t = ? (hint: this is a two-tailed test)

Should you reject the null hypothesis? (yes or no)

WEIGHT	STATUS
24.50	survived
26.90	survived
26.90	survived
24.30	survived
24.10	survived
26.50	survived
24.60	survived
24.20	survived
23.60	survived
26.20	survived
26.20	survived
24.80	survived
25.40	survived
23.70	survived
25.70	survived
25.70	survived
26.30	survived
26.70	survived
23.90	survived
24.70	survived
28.00	survived
27.90	survived
25.90	survived
25.70	survived
26.60	survived
23.20	survived
25.70	survived
26.30	survived
24.30	survived
26.70	survived
24.90	survived
23.80	survived
25.60	survived
27.00	survived
24.70	survived
26.50	perished
26.10	perished
25.60	perished
25.90	perished
25.50	perished
27.60	perished
25.80	perished
24.90	perished
26.00	perished
26.50	perished
26.00	perished
27.10	perished
25.10	perished
26.00	perished
25.60	perished
25.00	perished
24.60	perished
25.00	perished
26.00	perished
28.30	perished
24.60	perished
27.50	perished
31.10	perished
28.30	perished

Expert Solution

The null and alternative hypothesis:

; the true mean weight of sparrow that perished and survived are not different.

; the true mean wright of sparrow that perished and survived are different.

true mean weight of sparrow that perished

true mean weight of sparrow that survived

Based on the sample we have calculated the sample mean and sample variance as follows:

	Perished	Survived
Sample mean
Sample variance
sample size

To test this hypothesis we use a Two sample t-test with EQUAL VARIANCE.

The formula for test-statistic is:

; with

where Pooled variance

Calculation for :

Calculation for test-statistic:

The test-statistic is calculated as

Critical value:

,

Decision:

Since,

Conclusion:

At the data does provide enough evidence to support the alternative hypothesis, i.e.,

So we conclude that the true mean weight of sparrow that perished and survived is significantly different.

orchestra answered 1 year ago

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