Gregor Mendel has been called the father of genetics, having formulated laws of
ID: 3133714 • Letter: G
Question
Gregor Mendel has been called the father of genetics, having formulated laws of inheritance even before the function of DNA was discovered. In one famous experiment with peas, he crossed pure breeds of plants producing smooth peas and plants producing wrinkled peas. The first-generation peas were all smooth. In the second generation (F2), he obtained 5474 smooth peas and 1850 wrinkled peas. Do these data agree with the conclusion of 75% dominant trait (in this case smooth) occurrence in F2? Follow the four-step process as illustrated in Example 19.6.
Give the value of the z statistic.
Give your answer to 3 decimal places, including sign.
Fill in the blank:
Explanation / Answer
One sample z test for population proportion
Here, we are given n = 5474 + 1850 = 7324
Favourable peas = X = 5474
The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: The population proportion for smooth peas is 75%.
Alternative hypothesis: Ha: The population proportion for smooth peas is not 75%.
Symbolically, we write this hypothesis as below:
H0: P = 0.75 versus Ha: P 0.75
Here, we assume the level of significance or the value of alpha as 0.05 or 5%.
The test statistic formula for this test is given as below:
Z = ( p – P) / sqrt(PQ/n)
Here, p = 5474/7324 = 0.7474
P = 0.75, Q = 1 – P = 1 – 0.75 = 0.25 and n = 7324
Now, plug all values in the above formula
Z = ( 0.7474 – 0.75) / sqrt (0.75*0.25/7324) = -0.5127
Z Test of Hypothesis for the Proportion
Data
Null Hypothesis p =
0.75
Level of Significance
0.05
Number of Items of Interest
5474
Sample Size
7324
Intermediate Calculations
Sample Proportion
0.747405789
Standard Error
0.0051
Z Test Statistic
-0.5127
Two-Tail Test
Lower Critical Value
-1.9600
Upper Critical Value
1.9600
p-Value
0.6081
Do not reject the null hypothesis
Here, we get the p-value greater than the given level of significance or alpha value, so we do not reject the null hypothesis that that the population proportion for smooth peas is 75%.
Z Test of Hypothesis for the Proportion
Data
Null Hypothesis p =
0.75
Level of Significance
0.05
Number of Items of Interest
5474
Sample Size
7324
Intermediate Calculations
Sample Proportion
0.747405789
Standard Error
0.0051
Z Test Statistic
-0.5127
Two-Tail Test
Lower Critical Value
-1.9600
Upper Critical Value
1.9600
p-Value
0.6081
Do not reject the null hypothesis
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