Ha: μ ≠ 30 we know that the sample standard deviation is 10 and the sample size is 70. for what sample mean would the p-value be equal to 0.05? assume that all conditions necessary for inference are satis fied.

From the given problem the same size is n = 70. Df = n - 1 = 70 - 1 = 69.

The population mean is u = 30, sample standard deviation is s = 10 and the sample size is n = 70. Then,

t = x - u / s sqrt of n

1.995 = x - 30 / (10 sqrt of 70)

1.995 = x - 30 / 1.1952

X - 30 = 1.995 (1.1952)

X - 30 = 2.3844

X = 30 + 2.3844

X = 32.3844

The sample mean is 32.3844