A random sample of size 20 drawn from a normal distribution has a sample mean of 8 and a sample standard deviation of 4.

A) Compute the sample test statistic t under the null hypothesis H_0: Mue(mean)=7
B) State the alternate hypothesis if you believe that the population mean may be more than 7.

A) To compute the sample test statistic t, we can use the formula:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

In this case, the sample mean is 8, the hypothesized mean is 7, the sample standard deviation is 4, and the sample size is 20. Plugging these values into the formula, we have:

t = (8 - 7) / (4 / sqrt(20))

Calculating the square root of 20, we get approximately 4.472. Now, let's substitute the values:

t = 1 / (4 / 4.472)
= 1 / 0.894
≈ 1.119

Therefore, the sample test statistic t under the null hypothesis H_0: μ(mean) = 7 is approximately 1.119.

B) If you believe that the population mean may be more than 7, the alternative hypothesis can be stated as H_A: μ(mean) > 7.