The article \"Well-Fed Crickets Bowl Maidens Over\" (Nature Science Update, Febr

Question

The article "Well-Fed Crickets Bowl Maidens Over" (Nature Science Update, February 11, 1999) reported that female field crickets are attracted to males that have 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 chirp rate was related to nutritional status, investigators fed male crickets a high protein diet for 8 days, after which chirp rate was measured. The mean chirp rate for the crickets on the high protein diet was reported to be 109 chirps per second. Is this convincing evidence that the mean chirp rate for crickets on a high protein diet is greater than 60 (which would then imply an advantage in attracting the ladies)? Suppose that the sample size and sample standard deviation are n = 32 and s = 40. We test the relevant hypotheses with = .01.

Suppose that a second group of crickets was not fed the high-protein diet during the same time period, and the following data was observed: x = 72 chirps per second n = 30 and s = 40.

Given the same hypothesis test: H0: = 60, Ha: > 60, = .01, calculate the value of the t-statistic.

a. -1.64

b. 1.94    

c. 1.64

d. -1.34

Use the Appendix Table 4 to find a P-value and state your conclusions.

1. Because P-value < .01, we fail to reject H0. There is not enough evidence to conclude that the mean chirp rate is higher than 60.

2. Because P-value > .01, we reject H0. There is sufficient evidence to conclude that the mean chirp rate is higher than 60.    

3. Because P-value < .01, we fail to reject H0. There is sufficient evidence to conclude that the mean chirp rate is higher than 60.

4. Because P-value > .01, we fail to reject H0. There is not enough evidence to conclude that the mean chirp rate is higher than 60.

1. =mean chirp rate for crickets on a high protein diet 2. H0 : = 60 3. Ha: > 60 4. = .01 5.

6. This test requires a random sample and either a large sample or a normal population distribution. Because the sample size is large (n = 32), it is reasonable to proceed with the t test as long as we are willing to consider the 32 male field crickets in this study as if they were a random sample from the population of male field crickets. 7. Test statistic:

8. This is an upper-tailed test, so the P-value is the area under the t curve with df = 31 and to the right of 6.93. From Appendix Table 4, P-value 0. 9. Because P-value 0 which is less than the significance level, , we reject H0. There is convincing evidence that the mean chirp rate is higher for male field crickets that eat a high protein diet.

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   60  
Ha:    u   >   60  
              
As we can see, this is a    right   tailed test.  
Getting the test statistic, as              
              
X = sample mean =    72          
uo = hypothesized mean =    60          
n = sample size =    30          
s = standard deviation =    40          
              
Thus, t = (X - uo) * sqrt(n) / s =    1.643167673 = 1.64 [ANSWER, C]

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df = n - 1 =    29          
              
              
hence, the p value is, as this is right tailed,              
              
p =    0.055574274

Hence, P > 0.01, we FAIL TO REJECT THE NULL HYPOTHESIS.          

Thus,

OPTION 4. Because P-value > .01, we fail to reject H0. There is not enough evidence to conclude that the mean chirp rate is higher than 60. [ANSWER, 4]

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