Question

A genetic theory says that a cross between two pink flowering plants will produce red flowering plants 25% of the time. To test the theory, 100 crosses are made and 26 of them produce a red flowering plant. Is this strong evidence that the theory is wrong? Carry out the appropriate hypothesis test at the 5% significance level. The appropriate hypothesis for this test is H0: p = 0.25 vs. HA: p ≠ 0.25 H0: μ = 0.25 vs. HA: μ ≠ 0.25 H0: x = 0.25 vs. HA: x ≠ 0.25 H0: p̂ = 0.25 vs. HA: p̂ ≠ 0.25

The test statistic is _____ (to two places after decimal)

the p-value is ________ (to three places after decimal)

There ____ (is/ is not) enough statistical evidence to conclude that the theory is wrong.

Answer 1

Answer)

Ho : P = 0.25

Ha : P not equal to 0.25

N = 100

P = 0.25

First we need to check the conditions of normality that is if n*p and n*(1-p) both are greater than 5 or not

N*p = 25

N*(1-p) = 75

Both the conditions are met so we can use standard normal z table to estimate the P-Value

Test statistics z = (oberved p - claimed p)/standard error

Standard error = √{claimed p*(1-claimed p)/√n

Observed P = 26/100 = 0.26

Claimed P = 0.25

N = 100

After substitution

Test statistics z = 0.23

From z table, P(z>0.23) = 0.409

But our test is two tailed so, p-value is 2*0.409 = 0.818

As the obtained P-Value is greater than the given significance level, (0.05)

We fail to reject the null hypothesis

There is not enough statistical evidence to conclude that theory is wrong