Answer:
A
Null hypothesis: H0: p = 0.515
Alternative hypothesis: Ha ≠ 0.515
z = -0.257
P value = P(Z<-0.257) = 0.797
Decision; we fail to reject the null hypothesis. That is, the results support the belief that 51.5% of newborn babies are boys
Rule
If;
P-value > significance level --- accept Null hypothesis
P-value < significance level --- reject Null hypothesis
Z score > Z(at 90% confidence interval) ---- reject Null hypothesis
Z score < Z(at 90% confidence interval) ------ accept Null hypothesis
Step-by-step explanation:
The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.
For the case above;
Null hypothesis: H0: p = 0.515
Alternative hypothesis: Ha ≠ 0.515
Given;
n=850 represent the random sample taken
Test statistic z score can be calculated with the formula below;
z = (p^−po)/√{po(1−po)/n}
Where,
z= Test statistics
n = Sample size = 850
po = Null hypothesized value = 0.515
p^ = Observed proportion = 434/850 = 0.5106
Substituting the values we have
z = (0.5106-0.515)/√(0.515(1-0.515)/850)
z = −0.256677
z = −0.257
To determine the p value (test statistic) at 0.10 significance level, using a two tailed hypothesis.
P value = P(Z<-0.257) = 0.797
Since z at 0.10 significance level is between -1.645 and +1.645 and the z score for the test (z = -0.257) which falls with the region bounded by Z at 0.10 significance level. And also the one-tailed hypothesis P-value is 0.797 which is greater than 0.10. Then we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say that at 10% significance level the null hypothesis is valid.
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