Question

The sample birth weight of 16 infants in a local community is 7.5 lbs with a standard deviation of 1.5 lbs. A census has revealed that national birth weight is 6,5 lbs.

1. Compute the test statistic to test if the average birth weight in the local community differs from that of the national average. Leave your answer correct up to 3 decimal places.

2. State the critical value(s) to test the above hypothesis at alpha=.01

a. ± 2.947

b. 2.58

c. -2.947

d. -2.58

e. ± 2.58

f. 2.947

3. Calculate the minimum sample size to compute a 95% confidence interval for the true mean birth weight within half a 1 lb.

Answer 1

1)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (7.5 - 6.5)/(1.5/sqrt(16))
t = 2.667

2)

ejection Region
This is two tailed test, for α = 0.01 and df = 15
Critical value of t are -2.947 and 2.947.
Hence reject H0 if t < -2.947 or t > 2.947

+/- 2.947

3)

The following information is provided,
Significance Level, α = 0.05, Margin or Error, E = 0.5, σ = 1.5

The critical value for significance level, α = 0.05 is 2.131.

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (tc *σ/E)^2
n = (2.131 * 1.5/0.5)^2
n = 40.870

Therefore, the sample size needed to satisfy the condition n >=40.870

and it must be an integer number, we conclude that the minimum required sample size is n =41
Ans : Sample size, n = 41