Question

In: Statistics and Probability

A sample of 36 ten-year-old children provided their mean weight of 36.5 and a standard deviation...

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?

Expert Solution

(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.

orchestra answered 1 year ago

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