Question

A Canadian longitudinal study1 examined whether giving antibiotics in infancy increases the likelihood that the child will be overweight later in life. The study included children and found that of the children had received antibiotics during the first year of life. Test to see if this provides evidence that more than of Canadian children receive antibiotics during the first year of life. Show all details of the hypothesis test, including hypotheses, the standardized test statistic, the -value, the generic conclusion using a significance level, and a conclusion in context.
1. Clearly state the null and alternative hypotheses.
2. Calculate the test statistic and p-value.
3. What is the conclusion?
4. Do we have evidence to conclude that more than 70% of Canadian infants receive antibiotics?
A. Yes
B. No

Answer 1

Answer:

1. $H_{0}$ : p = 0.70 , $H_{a}$ : p > 0.70

2. Test Statistic : 0.54 , P value : 0.2946

3. Fail to reject null Hypothesis

4. No.

Step-by-step explanation:

1. Null hypothesis is 70% of children receive antibiotics.

Alternative hypothesis is more than 70% of children receive antibiotics.

2. Test statistic is calculated as;

z = $\frac{p (1 - p)}{\sqrt{\frac{p (1-p}{n} )} }$

z = $\frac{0.01}{0.0185}$

z = 0.54

3. p value is calculated as;

1 - right tailed probability

1 - 0.7054 = 0.2946