Bill Alther is a zoologist who studies Anna’s hummingbird (Calypte anna). A random sample of nine of these birds was caught, weighed, and released in a remote part of the Grand Canyon. The weights observed (in grams) were : 3.7 2.9 3.8 4.2 4.8 3.1 3.5 4.3 3.0 Let x be a random variable representing weights of Anna’s hummingbirds in this part of the Grand Canyon. Assuming x has a normal distribution with sample standard deviation 0.648. The population mean is 4.55 grams. (a) Calculate the Sample Mean of the above mentioned data values. (b) Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.55 grams? Establish the Null and Alternate Hypothesis. (c) Compute the Test statistics of the sample data using Student’s t-distribution table. Take = 0.05 (d) Find the P-value or range of P-values. (e) Conclude the test and interpret the result.
Q. NO 4
HYPOTHESIS TESTING FOR ONE POPULATION
Bill Alther is a zoologist who studies Anna’s hummingbird (Calypte anna). A random sample of nine of these birds was caught, weighed, and released in a remote part of the Grand Canyon. The weights observed (in grams) were :
3.7 2.9 3.8 4.2 4.8 3.1 3.5 4.3 3.0
Let x be a random variable representing weights of Anna’s hummingbirds in this part of the Grand Canyon. Assuming x has a
(a) Calculate the Sample Mean of the above mentioned data values.
(b) Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.55 grams? Establish the Null and Alternate Hypothesis.
(c) Compute the Test statistics of the sample data using Student’s t-distribution table. Take = 0.05
(d) Find the P-value or
(e) Conclude the test and interpret the result.
A researcher believes that the mean age of medical doctors in a large hospital system is older than the average age of doctors in the United States, which is 46. Assume the population standard deviation is 4.2 years. A random sample of 30 doctors from the system is selected, and the mean age of the sample is 48.6. Test the claim at α = 0.05
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