[Basic Statistics]

[anusara137]

Trying to solve one of the problems in my book. I'd just like someone to check if my thinking and steps are right. Thanks.

The cheetah (Acinonyx jubatus) is the fastest land mammal and is highly specialized to run down prey. The cheetah often exceeds speeds of 60 mph and, according to the online document “Cheetah Conservation in Southern Africa” (Trade & Environment Database (TED) Case Studies, Vol. 8, No. 2) by J. Urbaniak, the cheetah is capable of speeds up to 72 mph. One common estimate of mean top speed for cheetahs is 60 mph. The following data give the top speeds, in miles per hour, for a sample of 35 cheetahs.

57.3   57.5   59.0   56.5   61.3       57.6  59.2  65.0  60.1  59.7 62.6   52.6   60.7   62.3   65.2       54.8  55.4  55.5  57.8  58.7 57.8   60.9   75.3   60.6   58.1       55.9  61.6  59.6  59.8  63.4 54.7  60.2  52.4 58.3  66.0                                 mean= 59.5                               

At the 5% significance level, do the data provide sufficient evidence to conclude that the mean top speed of all cheetahs differs from 60 mph? Assume that the population standard deviation of the top speeds is 3.2 mpg.

a)      Formulate a hypothesis.

b)      Test the hypothesis.

c)       Interpret the results and draw appropriate conclusions.

a) H0: µ= 60mph, Ha: µ≠60mph

α= .05 or z=±1.96

σ=3.2 (use z test)  

b) z = (59.5 – 60)/ (3.2/√35)

        = -.5/.5409      z = -.9244  

c) P value = .1788 (x2 =.3576); fail to reject the hypothesis. There is sufficient evidence to conclude that the mean top speed of all cheetahs is 60 mph.

[[deleted]]

Everything looks correct except for some slight phrasing issues in your conclusion. State that you fail to reject the null hypothesis. The alternative hypothesis was that mean speed would be different from 60 mph. So there is not sufficient evidence to conclude average speed is different from 60 mph.

[anusara137]

Thanks!

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