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The average height of children who are 2 years old is 34 inches. A random sample of 35 children who are 2 years old in a large daycare franchise is collected, and they are found to average 29.50 inches with a standard deviation of 1.70 inches. The researchers are suspicious that the children at the daycare are not growing as quickly as they should be.
a. Write the hypotheses.
b. Calculate the test statistic.
c. Calculate the P-value
d. What is the conclusion for the hypothesis test?

Answer :

There is sufficient evidence to support the claim.

What is sufficient evidence ?

Sufficient evidence is admitted evidence that has enough overall weight, in terms of relevance and credibility, to legally justify a particular conclusion.

This is left tailed test .

The null and alternative hypothesis is ,

H0 :  mu= 34

Ha :mu < 34

Test statistic(t) = (x)

n= root (29.5 - 34) / 1.70

root 35

Test statistic = -15.66

P-value = 0

Alpha = 0.05

P-value <Alpha

Reject the null hypothesis .

There is sufficient evidence to support the claim.

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