The article “Well-Fed Crickets Bowl Maidens Over” (Nature Science Update, February 11, 1999) reported that female field crickets are attracted to males with high chirp rates and hypothesized that chirp rate is related to nutritional status. The usual chirp rate for male field crickets was reported to vary around a mean of 60 chirps per second. To investigate whether the chirp rate was related to nutritional status, investigators fed 27 male crickets a high protein diet for 8 days, after which chirp rate was measured. Let: The parameter μ be the mean chirp rate of male crickets on a high protein diet for 8 days. Given: The mean chirp rate for the random sample of crickets on the high protein diet was reported to be 64 chirps per second with a standard deviation of 14. Research Question: Is there convincing evidence that the mean chirp rate for crickets on a high protein diet implies an advantage in attracting the ladies? It is known that the researchers did not want to risk a Type I error of more than 5%. a) identify the alternative hypothesis b) Calculate the value of the test statistic. (4 decimal places) c) Find the upper boundary of a 95% confidence interval of the mean chirp of male field crickets that was on a high protein diet for 8 days. ( 2 decimal places)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 4AGP

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The article “Well-Fed Crickets Bowl Maidens Over” (Nature Science Update, February 11, 1999) reported that female field crickets are attracted to males with high chirp rates and hypothesized that chirp rate is related to nutritional status. The usual chirp rate for male field crickets was reported to vary around a mean of 60 chirps per second. To investigate whether the chirp rate was related to nutritional status, investigators fed 27 male crickets a high protein diet for 8 days, after which chirp rate was measured.

Let:

The parameter μ be the mean chirp rate
of male crickets on a high protein diet for 8 days.

Given:

The mean chirp rate for the random sample of crickets on the high protein diet was reported to be 64 chirps per second with a standard deviation of 14.

Research Question:

Is there convincing evidence that the mean chirp rate for crickets on a high protein diet implies an advantage in attracting the ladies?
It is known that the researchers did not want to risk a Type I error of more than 5%.

a) identify the alternative hypothesis

b) Calculate the value of the test statistic. (4 decimal places)

c) Find the upper boundary of a 95% confidence interval of the mean chirp of male field crickets that was on a high protein diet for 8 days. ( 2 decimal places)

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