To test Upper H0: muμequals=60 versus Upper H1: muμless than<60, 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. Click here to view the t-Distribution Area in Right Tail. (a) If x overbar x=57.5 and s=12.5 compute the test statistic. t 0=nothing (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the a=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: nothing (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. (c) Draw a t-distribution that depicts the critical region. Choose the correct answer below. A. t Subscript alphatα 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. B. negative t Subscript alpha−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. C. t Subscript alpha divided by 2tα/2 negative t Subscript alpha divided by 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. (d) Will the researcher reject the null hypothesis? A. No, because the test statistic does not fall in the critical region. B. Yes, because the test statistic falls in the critical region. C. No, because the test statistic falls in the critical region. D. Yes, because the test statistic does not fall in the critical region.

To test Upper H0: muμequals=60 versus Upper H1: muμless than<60, 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. Click here to view the t-Distribution Area in Right Tail. (a) If x overbar x=57.5 and s=12.5 compute the test statistic. t 0=nothing (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the a=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: nothing (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. (c) Draw a t-distribution that depicts the critical region. Choose the correct answer below. A. t Subscript alphatα 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. B. negative t Subscript alpha−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. C. t Subscript alpha divided by 2tα/2 negative t Subscript alpha divided by 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. (d) Will the researcher reject the null hypothesis? A. No, because the test statistic does not fall in the critical region. B. Yes, because the test statistic falls in the critical region. C. No, because the test statistic falls in the critical region. D. Yes, because the test statistic does not fall in the critical region.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

To test

Upper H0:

muμequals=60

versus

Upper H1:

muμless than<60,

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.

Click here to view the t-Distribution Area in Right Tail.

(a) If

x overbar x=57.5

and

s=12.5

compute the test statistic.

t 0=nothing

(Round to three decimal places as needed.)

(b) If the researcher decides to test this hypothesis at the

a=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:

nothing

(Round to three decimal places. Use a comma to separate answers as needed.)

t Subscript alphatα

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.

negative t Subscript alpha−tα

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.

t Subscript alpha divided by 2tα/2

negative t Subscript alpha divided by 2−tα/2

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.

(d) Will the researcher reject the null hypothesis?

No, because the test statistic does not fall in the critical region.

Yes, because the test statistic falls in the critical region.

No, because the test statistic falls in the critical region.

Yes, because the test statistic does not fall in the critical region.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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