In: Statistics and Probability
A sample of 36 ten-year-old children provided their mean weight of 36.5 and a standard deviation of 5 kg. Furthermore, it is known that the weight does not follow a normal distribution. Is there sufficient statistical evidence to infer that the population mean of the weight of 10-year-old children is greater than 35 kg? Uses a significance level of 0.005 a.) Write Ho y Ha b.) It indicates the region of acceptance and rejection of Ho c.) what is your hypothesis test conclusion?
(a)
H0: Null Hypothesis: 35 ( The population mean of the weight of 10-year-old children is not greater than 35 kg)
HA: Alternative Hypothesis: 35 ( The population mean of the weight of 10-year-old children is greater than 35 kg) (Claim)
(b)
n = 36
Even though it is known that the weight does not follow a normal distribution, the distribution of sample means is normal distribution by Central Limit Theorem sincesample size = n =36 > 30 Large sample.
= 36.5
s = 5
= 0.005
df = 36 - 1 = 35
From Table, critical value of t = 2.724
The region of acceptance of Ho : for t 2.724
The region of rejection of Ho : for t > 2.724
(c)
Test Statistic is given by:
Since calculated value of t = 1.80 is less than critical value of t =2.724, the difference is not significant. Fail to reject null hypothesis.
Conclusion:
The data do not support the claim that the population mean of the
weight of 10-year-old children is greater than 35 kg.