Versus H1​: μ<50​, a random sample of size n=24 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=47.3 and s=10.5​, compute the test statistic.
t0=

​(Round to three decimal places as​ needed.)
​(b) If the researcher decides to test this hypothesis at the α=0.05 level of​ significance, determine the critical​ value(s). Although technology or a​ t-distribution table can be used to find the critical​ value, in this problem use the​ t-distribution table given.
Critical​ Value:

​(Round to three decimal places. Use a comma to separate answers as​ needed.)
​(c) Draw a​ t-distribution that depicts the critical region. Choose the correct answer below.
A.
−tα
0

A symmetric bell-shaped curve is plotted over a horizontal axis with two labeled coordinates. The curve's center and peak are at 0, negative t Subscript alpha is to the left of 0, and two vertical lines run from the axis to the curve at 0 and negative t Subscript alpha. The area under the curve to the left of negative t Subscript alpha is shaded.
B.
tα/2−tα/2
0

A symmetric bell-shaped curve is plotted over a horizontal axis with three labeled coordinates. A vertical line runs from the axis to the curve's peak at 0. Two additional vertical lines, equidistant from 0, run from the axis to the curve at negative t Subscript (alpha divided by 2) and t Subscript (alpha divided by 2), which are respectively to the left and right of 0. The areas under the curve to the left of the leftmost vertical line and to the right of the rightmost vertical line are shaded.
C.
tα
0

A symmetric bell-shaped curve is plotted over a horizontal axis with two labeled coordinates. The curve's center and peak are at 0, t Subscript alpha is to the right of 0, and two vertical lines run from the axis to the curve at 0 and t Subscript alpha. The area under the curve to the right of t Subscript alpha is shaded.
​(d) Will the researcher reject the null​ hypothesis?