Question

A. If the population mean height for​ 3-year-old boys is 37 inches. Suppose a random sample of 15​ 3-year-old boys from Country B showed a sample mean of 36.1 inches with a standard deviation of 2 inches. The boys were independently sampled. Assume that heights are Normally distributed in the population.

a. Determine whether the population mean for Country B boys is significantly different from the Country A mean. Use a significance level of 0.05.

Find the test statistic t  = Answer ____ ​(Type an integer or decimal rounded to two decimal places as​ needed.)

Find the​ p-value = Answer ____ ​(Type an integer or decimal rounded to two decimal places as​ needed.)

B. Suppose the sample consists of 30 boys instead of 15 and repeat the test.

Find the test statistic. T= Answer _____ ​(Type an integer or decimal rounded to two decimal places as​ needed.)

Find the​ p-value = Answer______ ​(Type an integer or decimal rounded to three decimal places as​ needed.)

Answer 1

Answer)

Null hypothesis Ho : u = 37

Alternate hypothesis Ha : u not equal to 37

As the population s.d is unknown here and we are using sample s.d as the best estimate

We will use t distribution to conduct the test

Test statistics t = (sample mean - claimed mean)/(s.d/√n)

t = (36.1- 37) /(2/√15) = -1.74

Degrees of freedom is = n-1 = 14

For 14 dof and -1.74 test statistics

P-value from t distribution is = 0.1038

B)

Test statistics t = (36.1 - 37)/(2/√30) = -2.46

P-value for 14 dof and -2.46 test statistics from t distribution is = 0.0275