Question

Họ: > 15.7 H1 :μ < 15.7 Your sample consists of 32 values, with a sample mean of 14.7. Suppose the population standard deviation is known to be 2.97. a) Calculate the value of the test statistic, rounded to 4 decimal places. z = __________

b) At a = 0.07, the rejection region is O z > 1.8119 O z > 1.4758 O Z< -1.8119 or 2 > 1.8119 O z < -1.4758 or 2 > 1.4758 O Z< -1.8119 O Z< -1.4758 c) The decision is to Fail to reject the null hypothesis Accept the alternative hypotheis Accept the null hypothesis Reject the null hypothesis d) Suppose you mistakenly rejected the null hypothesis in this problem, what type of error is that?

Answer 1

a) To calculate the value of the test statistic, we use the formula:

z = (sample mean - population mean) / (population standard deviation / square root of sample size)

Substituting the given values, we get:

z = (14.7 - 15.7) / (2.97 / sqrt(32))
z = -2.8284

Rounding to 4 decimal places, we get:

z = -2.8284

b) The rejection region is given as z > 1.8119 at a significance level of 0.07. Since our calculated value of z is -2.8284, it falls in the rejection region. Therefore, we can reject the null hypothesis.

c) The decision is to Reject the null hypothesis.

d) If we mistakenly rejected the null hypothesis, that would be a Type I error.