A genetic experiment involving peas yielded one sample of offspring consisting o

Question

A genetic experiment involving peas yielded one sample of offspring consisting of 448 green peas and 127 yellow peas. Use a 0.05 significance level to test the claim that under the same circumstances, 27% of offspring peas will be yellow. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim. Use the P-value method and the normal distribution as an approximation to the binomial distribution.

Explanation / Answer

as p value is less than 0.05 level of significance we reject null hypothesis

we have sufficient evidence to conclude that  offspring peas that will be yellow is different from 27%.

null Hypothesis:               Ho:    p = 0.2700 alternate Hypothesis:    Ha:    p 0.2700 for 0.1 level with two tailed test , critical value of z= 1.6449 Decision rule :                   reject Ho if absolute value of test statistic |z|>1.645 sample success                                                           x                    = 127 sample size n                    = 575 std error       =Se            =(p*(1-p)/n) = 0.0185 sample proportion     p x/n= 0.2209 test stat = z                =                        (p-p)/Se= -2.6536 p value                                                      = 0.0080

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