Acompany wants to establish that the mean life of its batteries, when used in a wireless mouse, is over 183 days. the data will consist of the life lengths of batteries in 64 different wireless mice.

a) formulate the null and alternative hypotheses.

b) if the true mean is 190 days, what error can be made?

a) Null and alternative hypotheses are:

: mu=183 days

: mu>183 days

b) If the true mean is 190 days, Type II error can be made.

Step-by-step explanation:

Let mu be the mean life of the batteries of the company when it is used in a wireless mouse

Null and alternative hypotheses are:

: mu=183 days

: mu>183 days

Type II error happens if we fail to reject the null hypothesis, when actually the alternative hypothesis is true.

That is if we conclude that mean life of the batteries of the company when it is used in a wireless mouse is at most 183 days, but actually mean life is 190 hours, we make a Type II error.

see the explanation

Step-by-step explanation:

we know that

An isosceles triangle has two equal sides and two equal angles

step 1

Find the measure of angle BDA

we know that

Triangle ABD is an isosceles triangle

AB=AD ---> given problem

so

m∠ABD=m∠BDA

therefore

m∠BDA=72°

step 2

Find the measure of angle BAD

Remember that the sum of the interior angle in a triangle must be equal to 180 degrees

In the triangle BDA

m∠ABD+m∠BDA+m∠BAD=180°

substitute the given values

72°+72°+m∠BAD=180°

144°+m∠BAD=180°

m∠BAD=180°-144°=36°

step 3

Find the measure of angle BCA

In the triangle ABC

m∠BCA=m∠BAC

we have that

m∠BAC=m∠BAD=36°

therefore

m∠BCA=36°

step 4

Find the measure of angle ABC

In the triangle ABC

m∠BAC+m∠BCA+m∠ABC=180°

substitute the given values

36°+36°+m∠ABC=180°

72°+m∠ABC=180°

m∠ABC=180°-72°=108°

step 5

Find the measure of angle DBC

we know that

m∠DBC+m∠ABD=m∠ABC ----> by addition angle postulate

substitute the given values

m∠DBC+72°=108°

m∠DBC=108°-72°=36°

step 6

Find the measure of angle BDC

we know that

m∠BDC+m∠ADB=180° ----> by supplementary angles

substitute the given value

m∠BDC+72°=180°

m∠BDC=180°-72°=108°

step 7

In the triangle DBC we have

m∠DBC=36°

m∠BCD=m∠BCA=36°

so

The triangle BCD has two equal angles

therefore

Triangle BCD is an isosceles triangle

and

BD=BC