Mathematics, 20.07.2021 01:20, Liantic34

Provided below are summary statistics for independent simple random samples from two populations. Use the pooled t-test and the pooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval. x1=21, s1=4, n1=12, x2=20, s2=3, n2=15
A. What are the correct hypotheses for a right-tailed test?
b. Compute the test statistic.
c. Determine the P-value.
B. The 90% confidence interval is from to .

Answers: 2

Show answers

Answers

answered: mooneyhope24

(a) $H_o:\mu_1 = \mu_2$ $H_a:\mu_1 \mu_2$

(b) t = 0.74

(d) CI = (-2.095,4.095)

Step-by-step explanation:

Given

$\bar x_1=21,\ s_1=4,\ n_1=12,\\ \bar x_2=20,\ s_2=3,\ n_2=15$

Solving (a): The hypotheses

The test is right-tailed, means that the alternate hypothesis will contain greater than sign.

So, we have:

$H_o:\mu_1 = \mu_2$

$H_a:\mu_1 \mu_2$

Solving (b); The test statistic (t)

This is calculated as:

$t = \frac{\bar x_1 - \bar x_2}{\sqrt{\frac{s_1^2(n_1 - 1) + s_2^2(n_2 - 1)}{n_1 + n_2 - 2} * (\frac{1}{n_1} + \frac{1}{n_2})}}$

So, we have:

$t = \frac{21 - 20}{\sqrt{\frac{4^2(12 - 1) + 3^2(15 - 1)}{12 + 15 - 2} * (\frac{1}{12} + \frac{1}{15})}}$

$t = \frac{1}{\sqrt{\frac{302}{25} * (0.15)}}$

$t = \frac{1}{\sqrt{12.08 * 0.15}}$

$t = \frac{1}{\sqrt{1.812}}$

$t = \frac{1}{1.346}$

t = 0.74

Solving (c): The P-value

First, we calculate the degrees of freedom

df = n_1 + n_2 -2

df = 12+15 -2

df = 25

Using the t distribution, the p-value is:

p =TDIST(0.74,25)

p =0.2331

Solving (d): The 90% confidence interval

Calculate significance level

$\alpha = 1 - CI$

$\alpha = 1 - 90\%$

$\alpha = 0.10$

Calculate the t value (t*)

$t^* = (\alpha/2,df)$

t^* = (0.10/2,25)

t^* = (0.05,25)

t^* = 1.708

The confidence interval is calculated using:

$CI = (\bar x - \bar x_2) \± t^* *\sqrt{\frac{s_1^2(n_1 - 1) + s_2^2(n_2 - 1)}{n_1 + n_2 - 2} * (\frac{1}{n_1} + \frac{1}{n_2})}$

$CI = (21 - 20) \± 1.708 *\sqrt{\frac{4^2(12 - 1) + 3^2(15 - 1)}{12 + 15 - 2} * (\frac{1}{12} + \frac{1}{15})}$

$CI = 1 \± 1.708 *1.812$

$CI = 1 \± 3.095$

Split

$CI = 1 - 3.095 \ or\ 1 + 3.095$

$CI = -2.095 \ or\ 4.095$

CI = (-2.095,4.095)

answered: Guest

the clues that signal the reader should change tone are the punctuation marks, the grammatical signs. for example, the quotation marks at the beginning of something someone else said literally or the exclamation marks.

the tone of the first line of dialogue until "gettysburg" is a kind tone, a tone of advise. the narrator is trying to the other person in doing something he or she obviously is finding hard to do by giving a piece of advise and bringing up a memory of a successful similar case.

the clue that the reader understand how to read the word "bang" is the exclamation mark. it gives the word a surprise tone, a strong accent.

the best tone for reading the word "bang" is an exciting tone, a surprise one, even a loud one.

the words that should be read with a formal tone are the ones that give factual information. the sentence: mister lincoln couldn't think of anything to say at the gettysburg" gives information about an event and it needs to be read formally, also, when the narrator wants to transmit calmness, a formal and slow tone is needed, because people also transmit messages with the vibrations of our voices and tones.

answered: Guest

the best buy, is the 4- kilogram bag of lollipops for $18.40.

step-by-step explanation:

i found my answer by dividing the cost of each bag by their respective weights.

14.88 divided by 2 = 7.44

17.29 divided by 3 = 5.77

18.4 divided by 4 = 4.6

24.4 divided by 5 = 4.88

by this, i found that the 4 kilo bag is the best buy.