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 26 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.
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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
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 64.04 chirps per second with a standard deviation of 10.
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%.
Alternative hypothesis.
- H1:μ>60
Test statistic = 2.0600
a) Find the critical value for the appropriate test statistic. (3 decimal places)
__________
b) Choose the correct interval for the p-value:
- 0<p-value ≤0.005
- 0.005<p-value ≤0.01
- 0.01<p-value ≤0.025
- 0.025<p-value ≤0.05
- 0.05<p-value ≤0.1
- p-value >0.1
c) Find the lower boundary of a 95% confidence interval of the mean chirp rate of male field crickets that was on a high protein diet for 8 days.
_____________ (2 decimal places)
d) According to the critical value approach, it is evident that the null hypothesis is _____ (rejected/not rejected) and there is _______ (enough evidence/not enough evidence) that the mean chirp rate is higher for male field crickets that eat a high protein diet.
Given data :
sample size, n = 26
sample mean, x̄ = 64.04
sample standard deviation,s= 10.0
population mean,μ= 60.0
Significance level, α= 0.05
Hypothesis test :
The null and alternative hypothesis is
H0: u = 60.0
Ha: u > 60.0
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