Answer:
Explanation:
This is a test of 2 independent groups. The population standard deviations are not known. it is a two-tailed test. Let m be the subscript for the number of English courses taken by male students and f be the subscript for the number of English courses taken by female students.
Therefore, the population means would be μm and μf.
The random variable is xm - xf = difference in the sample mean number of English courses taken by male and female students.
We would set up the hypothesis.
The null hypothesis is
H0 : μm = μf H0 : μm - μf = 0
The alternative hypothesis is
H1 : μm ≠ μf H1 : μm - μf ≠ 0
Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is
(xm - xf)/√(sm²/nm + sf²/nf)
From the information given,
xm = 3
xf = 4
sm = 0.8
sf = 1
nm = 29
nf = 16
t = (3 - 4)/√(0.8²/29 + 1²/16)
t = - 11.82
The formula for determining the degree of freedom is
df = [sm²/nm + sf²/nf]²/(1/nm - 1)(sm²/nm)² + (1/nf - 1)(sf²/nf)²
df = [0.8²/29 + 1²/16]²/[(1/29 - 1)(0.8²/29)² + (1/16 - 1)(1²/16)²] = 0.00715/0.00027781093
df = 25.7
Approximately, df = 26
We would determine the probability value from the t test calculator. It becomes
p value = 0.00001
Assuming a level of significance of 0.05, we would reject the null hypothesis because the p value, 0.00001 is < 0.05
Therefore, we can conclude that the means are not statistically the same.