Question

To test Upper H 0​: muequals100 versus Upper H 1​: munot equals​100, a simple random sample size of nequals16 is obtained from a population that is known to be normally distributed. Answer parts​ (a)-(d). LOADING... Click here to view the​ t-Distribution Area in Right Tail. ​(a) If x overbarequals105.1 and sequals8.8​, compute the test statistic. tequals nothing ​(Round to three decimal places as​ needed.) ​(b) If the researcher decides to test this hypothesis at the alphaequals0.01 level of​ significance, determine the critical values. The critical values are nothing. ​(Use a comma to separate answers as needed. Round to three decimal places as​ needed.) ​(c) Draw a​ t-distribution that depicts the critical​ region(s). Which of the following graphs shows the critical​ region(s) in the​ t-distribution? A. A symmetric bell-shaped curve is plotted over a horizontal axis. Two vertical lines, equidistant from the curve's peak at the center, extend from the axis to the curve on the far left and right sides of the graph. The areas under the curve to the left of the left vertical line and to the right of the right vertical line are shaded. B. A symmetric bell-shaped curve is plotted over a horizontal axis. On the far left side of the graph, a vertical line runs from the axis to the curve. The area under the curve to the left of the vertical line is shaded. C. A symmetric bell-shaped curve is plotted over a horizontal axis. On the far right side of the graph, a vertical line runs from the axis to the curve. The area under the curve to the right of the vertical line is shaded. ​(d) Will the researcher reject the null​ hypothesis? A. The researcher will reject the null hypothesis since the test statistic is between the critical values. B. There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic is not between the critical values. C. The researcher will reject the null hypothesis since the test statistic isnbsp not nbspbetween the critical values. D. There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic isnbspbetween the critical values.

Answer 1

Solution:
Given:

The null and alternative hypothesis are:

simple random sample size = n =16

Part a) Compute t test statistic

s = 8.8

Part b) If the researcher decides to test this hypothesis at the level of​ significance, determine the critical values.

Look in t table for two tail area= 0.01 and df = n - 1 = 16 - 1 =15

and find t critical value.

t critical value = 2.977

Since this is two tailed test , we have two critical values: ( -2.977 , 2.977 )

Part c) Draw a​ t-distribution that depicts the critical​ region(s).

Thus option A) is correct.

Part d) Will the researcher reject the null​ hypothesis?

Since t test statistic value is = t= 2.318 is not in critical region, we fail to reject H0.

Thus correct option is:

D. There is not sufficient evidence for the researcher to reject the null hypothesis since the test statistic is between the critical values.