Question

For each of the following, please show the following to receive full credit. (Answers without these steps will not be given credit)

(a) Draw a curve and label each part to reflect a left, right, or two-tailed test

(b) Claim: Show in symbols H0, Ha

(c) Critical value- find the z0 or t0 values

(d) What are the standardized test statistic z or t, and the P values from the calculator?

(e) Comparing the critical values, α value, against the calculator results, state whether you reject, or fail to reject the null hypothesis

(f) Interpret the decision in the context of the original claim.

A marine biologist claims that the mean dive duration of a harbor seal in Monterey Ba is at least 5.8 minutes. A random sample of 35 dive durations has a mean of 4.9 minutes and a standard deviation of 1.8 minutes. Is there enough evidence to reject the claim at α = 0.01?

Answer 1

a)

(Left tail test)

b)

Ho :   µ =   5.8  
Ha :   µ <   5.8  

c)
          
Level of Significance ,    α =    0.010  

critical t value, t* =        -2.4411   [Excel formula =t.inv(α/no. of tails,df) ]

d)

sample std dev ,    s =    1.8000  
Sample Size ,   n =    35  
Sample Mean,    x̅ =   4.9000  
          
degree of freedom=   DF=n-1=   34  
          
Standard Error , SE = s/√n =   1.8/√35=   0.3043  
t-test statistic= (x̅ - µ )/SE =    (4.9-5.8)/0.3043=   -2.958  
          
p-Value   =   0.0028   [Excel formula =t.dist(t-stat,df) ]

e)

Decision:   p-value≤α, Reject null hypothesis

f)

  
Conclusion: There is enough evidence to conclude that  the mean dive duration of a harbor seal in Monterey Ba is at least 5.8 minutes.

Please let me know in case of any doubt.

Thanks in advance!

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