1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Helga [31]
3 years ago
14

A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. Assume that the distr

ibutions follow the normal probability distribution and the population standard deviations are equal. The information is summarized below.
Statistic: Men Women
The sample mean: 24.51 22.69
Sample standard deviation: 4.48 3.86
Sample size: 35 40
At the 0.01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month?
a. State the decision rule for 0.01 significance level: H0: μMen= μWomen H1: μMen ≠ μWomen. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)
Reject H0 if t < _____ or t > ______
b. Compute the value of the test statistic. (Round your answer to 3 decimal places.)
c. What is your decision regarding the null hypothesis?
d. What is the p-value?
Mathematics
1 answer:
Marianna [84]3 years ago
4 0

Answer:

(a) Decision rule for 0.01 significance level is that we will reject our null hypothesis if the test statistics does not lie between t = -2.651 and t = 2.651.

(b) The value of t test statistics is 1.890.

(c) We conclude that there is no difference in the mean number of times men and women order take-out dinners in a month.

(d) P-value of the test statistics is 0.0662.

Step-by-step explanation:

We are given that a recent study focused on the number of times men and women who live alone buy take-out dinner in a month.

Also, following information is given below;

Statistic : Men      Women

The sample mean : 24.51      22.69

Sample standard deviation : 4.48    3.86

Sample size : 35    40

<em>Let </em>\mu_1<em> = mean number of times men order take-out dinners in a month.</em>

<em />\mu_2<em> = mean number of times women order take-out dinners in a month</em>

(a) So, Null Hypothesis, H_0 : \mu_1-\mu_2 = 0     {means that there is no difference in the mean number of times men and women order take-out dinners in a month}

Alternate Hypothesis, H_A : \mu_1-\mu_2\neq 0     {means that there is difference in the mean number of times men and women order take-out dinners in a month}

The test statistics that would be used here <u>Two-sample t test statistics</u> as we don't know about the population standard deviation;

                      T.S. =  \frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{s_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2}  } }  ~ t__n_1_-_n_2_-_2

where, \bar X_1 = sample mean for men = 24.51

\bar X_2 = sample mean for women = 22.69

s_1 = sample standard deviation for men = 4.48

s_2 = sample standard deviation for women = 3.86

n_1 = sample of men = 35

n_2 = sample of women = 40

Also,  s_p=\sqrt{\frac{(n_1-1)s_1^{2}+(n_2-1)s_2^{2}  }{n_1+n_2-2} }  =  \sqrt{\frac{(35-1)\times 4.48^{2}+(40-1)\times 3.86^{2}  }{35+40-2} } = 4.16

So, <u>test statistics</u>  =  \frac{(24.51-22.69)-(0)}{4.16 \sqrt{\frac{1}{35}+\frac{1}{40}  } }  ~ t_7_3

                              =  1.890

(b) The value of t test statistics is 1.890.

(c) Now, at 0.01 significance level the t table gives critical values of -2.651 and 2.651 at 73 degree of freedom for two-tailed test.

Since our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.

Therefore, we conclude that there is no difference in the mean number of times men and women order take-out dinners in a month.

(d) Now, the P-value of the test statistics is given by;

                     P-value = P( t_7_3 > 1.89) = 0.0331

So, P-value for two tailed test is = 2 \times 0.0331 = <u>0.0662</u>

You might be interested in
The frequency table below shows the hourly wages of 22 factory workers. How many are paid $10.50 per hour or more?
wel
The answer would be 11.
I hope that this will help somebody :)
8 0
3 years ago
Given that D(x) = 2x, select all of the following that are true statements.
GaryK [48]
It is D
You welcome
8 0
2 years ago
Shape 1 is similar to shape 2
melamori03 [73]

Yes it is, and don't worry, I hate school too! Amazing username!

8 0
3 years ago
Write in standard form: 22.2 x 10^5
garri49 [273]
2220000
 
it just means that 22.2 needs to be multiplied by 10, 5 times, so just move the decimal five to the right.
3 0
3 years ago
Can someone help me?
Romashka [77]

Answer:

I hope this helps!

Step-by-step explanation:

1. M is .25

b is 20

so

y= .25x+20

2. y= 3x+2

6 0
3 years ago
Other questions:
  • In the number 1934 is a value of 9 in 100 place 10 times the value of the 3 in the tens place
    13·1 answer
  • Which expression is equivalent to 15 y - 8 y​ ?
    9·2 answers
  • An open box with a volume of 1500 cm cube is to be constructed by taking a piece of cardboard 20 cm by 40 cm, cutting squares of
    7·1 answer
  • If x is the probability of an event happening, then which of the following represents x?
    8·1 answer
  • How do you solve questions 5,7 and 9 in the picture?
    14·1 answer
  • A population of insects increases at a rate of 1.5% per day. About how long will it take the population to double?
    13·2 answers
  • Find the area of a regular octagon with side length 6 cm
    10·2 answers
  • Order the numbers from least to greatest. 9/5, -2.5,-1.1, -4/5, 0.8
    7·1 answer
  • Please help me understand and explain it to me please.<br><br>Recursive Sequence Function ​
    7·1 answer
  • 8. In the diagram, the measure of the arc from A to B not
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!