Question

A botanist has produced a new variety of hybrid wheat that is better able to withstand drought than other varieties. The botanist knows that for the parent plants, the proportion of seeds germinating is 80%. The proportion of seeds germinating for the hybrid variety is unknown, but the botanist claims that it is 80%. To test this claim, 400 seeds from the hybrid plant are tested, and it is found that 312 germinate. Use a 5% level of significance to test the claim that the proportion germinating for the hybrid is 80%.

If the calculated value of test statistics was -1.00, what is the conclusion of the test?

Group of answer choices

Fail to Reject Alternative Hypothesis

Fail to Reject Null Hypothesis

None of above

Reject Null Hypothesis

Reject Alternative Hypothesis

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.80

Ha : p 0.80

n = 400

x =312

= x / n = 312 / 400 =0.78

P0 = 0.80

1 - P0 = 1 - 0.80 = 0.20

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.78 -0.80 / [(0.80*0.20) / 400]

= -1.00

Test statistic = z = -1.00

P-value = 2 * 0.1587 =0.3174

= 0.05

P-value >

0.3174 > 0.05

Fail to Reject Null Hypothesis

There is sufficient evidence to suggest that