Question

To test Upper H 0​: muequals40 versus Upper H 1​: muless than40​, a random sample of size nequals22 is obtained from a population that is known to be normally distributed. Complete parts​ (a) through​ (d) below. LOADING... Click here to view the​ t-Distribution Area in Right Tail. ​(a) If x overbarequals36.9 and sequals14.7​, compute the test statistic. t 0equals nothing ​(Round to three decimal places as​ needed.)

Answer 1

Answer 2

To compute the test statistic, we can use the formula for the one-sample t-test:

t = (x̄ - μ) / (s / √n)

Given the following values: x̄ = 36.9 (sample mean) s = 14.7 (sample standard deviation) n = 22 (sample size)

We are testing the null hypothesis that μ (population mean) equals 40 against the alternative hypothesis that μ is less than 40.

Substituting the values into the formula, we get:

t = (36.9 - 40) / (14.7 / √22)

Calculating the expression inside the parentheses first: (36.9 - 40) = -3.1

Next, calculating the denominator: (14.7 / √22) ≈ 3.127

Now, dividing the numerator by the denominator: t = -3.1 / 3.127

Calculating this division: t ≈ -0.99

Therefore, the test statistic is approximately -0.99. (Rounded to three decimal places as needed.)