Mathematics, 13.03.2020 01:30 thedragontale1020

Based on a random sample of 25 units of product X, the average weight is 102 lb and the sample standard deviation is 10 lb. We would like to decide whether there is enough evidence to establish that the average weight for the population of product X is greater than 100 lb. Assume the population is normally distributed. Using the critical value rule, at α = .01. What is the appropriate conclusion at 99% confident level?

Answers: 3

Show answers

Answers

Answer from: DangeRz

$t=\frac{102-100}{\frac{10}{\sqrt{25}}}=1$

$t_{crit}= 2.49$

Since the calculated value is lower than the critical value we have enough evidence to FAIL to reject the null hypothesis

So then we can conclude that the population mean is not significantly higher than 100

Step-by-step explanation:

Data given and notation

$\bar X=102$ represent the mean score for the sample

s=10 represent the standard deviation for the sample

n=25 sample size

$\mu_o =100$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

p_v represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the mean is higher than 100, the system of hypothesis would be:

Null hypothesis: $\mu \leq 100$

Alternative hypothesis: $\mu 100$

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

Calculate the critical value

We need to find the degrees of freedom first, given by:

df= n-1= 25-1 = 24

Since we are conducting a right tailed test we need to find a critical value on the t distribution with 24 degrees of freedom that accumulates 0.01 of the area on the right and we got:

$t_{crit}= 2.49$

Since the calculated value is lower than the critical value w have enough evidence to FAIL to reject the null hypothesis

So then we can conclude that the population mean is not significantly higher than 100

Answer from: Quest

overpriced

step-by-step explanation:

Answer from: Quest

Hello! i hope this
since the cosine is the ratio of the adjacent side to the hypotenuse, you can see that cos 60° = ½. answer. according to the property of cofunctions (topic 3), sin 30° is equal to cos 60°. sin 30° = ½.

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 18:10, TrueMonster8911

What is the equation in slope-intercept form of the linear function represented by the table? y -18 -1 -8 4 2 912 o y=-2x-6 o y=-2x+6 o y=2x-6 o y = 2x+6

Answers: 1

continue

Mathematics, 21.06.2019 20:30, NetherisIsTheQueen

What is always true about a positive integer raised to a negative odd power?

Answers: 1

continue

Mathematics, 21.06.2019 22:30, HappyPom4169

]supplementary angles are two angles that add up to . • complementary angles are two angles that add up to degrees. • adjacent angles share a and a • congruent angles have the measure. • an triangle has one angle that is greater than 90 degrees. • a triangle with angles 45°, 45°, and 90° would be a triangle

Answers: 2

continue

Mathematics, 21.06.2019 23:00, Pankhud5574

Is a square always, sometimes, or never a parallelogram

Answers: 2

continue

You know the right answer?

Based on a random sample of 25 units of product X, the average weight is 102 lb and the sample stand...