Question 193283
A biologist knows that the average length of a leaf of a certain full-grown plat is 4 inches. The standard deviation of the population is 0.6 inch. A sample of 20 leaves of that type of plant given a new type of plant food had an average lenght of 4.2 inches. Is there reason to believe that the new food is responsible for a change in the growth of the leaves? use α=0.01. Find the 99% confidence interval of the mean. DO the results occur? Explain. Assume that the variable is approximately normally distributed. 
My answer, Ho:µ = 4 and H1:µ ≠4: C.V.= ±2.58
z=1.49; 3.85<µ<4.55; do not reject. There is not enough evidence to support the cail that the growth has change. Is this correct? 
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Yes, if you are allowed to use a-scores for mean problems.
Most texts require that you use t-scores.
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10.) The tennis Industry Association reported that 14% of tennis fans were female. If, in a sample of 30 tennis fans, 15 were female, do the results suggest that the percentage may have changed? use &#945; = 0.02. 
Please help me with this problems. Thanks. 
Ho: p = 0.14
H1: p is not equal to 0.14
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test statistic: z(15/30) = ((0.5)-0.14)/sqrt[0.14*0.86/30] = 5.6826
Critical value for 2-tail test with alpha = 0.02 : z= +/-2.326
p-value: 2P(z > 5.6826) = 0.00000000665
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Conclusion: since the test stat. is in the reject interval, reject Ho.
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Cheers,
Stan H.