Part 1:
Based on the given data,
1.
The best estimate of population mean () would be the sample mean (). Hence, to estimate the mean no. of annual sea kills, we may make use of the given sample of size 51 and compute the mean no. of annual sea kills in the sample.
We get
2. The 100 (1-) % CI for population mean can be obtained by the formula:
For
We get the critical value of t as 2.009.
3. Substituting the values:
We get s = 53.71
= (259.56, 289.78)
Part 2:
1. Let denote the mean age at which the infant first speaks. We have to test:
Vs
2. From the given data,
3. The appropriate statistical test to test the above hypothesis would be a one sample t test.
But before running this test, we must ensure that the data satisfies the assumptions of this test:
- The data is continuous - The observations are independent - The data is normally distributed - There are no outliers
Assuming that all the assumptions are satisfied:
The test statistic is given by:
with critical region given by: for right tailed test.
a.
The critical value of t is given by:
Using excel,
(................Since, excel function gives only the two tailed probabilities, we must convert the one tailed 0.05 into two tailed 0.05*2 = 0.10)
We get
Substituting the values obtained in the test statistic:
= 2.56
4. To compute the p-value:
We get p-value = 0.0062
5. Since, the p-value of the test 0.0062 < 0.05, we may reject H0. We may conclude that the data provides sufficient evidence to support the claim that the mean age at which the infant first speaks is greater than 7 months.
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