In a head-to-head taste test of store-brand foods versus national brands, a company found that it was hard to find a taste difference in the two. If the national brand is indeed better than the store brand, it should have been judged as better more than 50% of the time but that conclusion could not be confirmed. However, if the store brand has a better taste than the national brand, then the store brand should be judged as better more than 50% of the time. Test the hypothesis that the store-brand has a better taste than the national brand.

We fail to reject the null hypothesis.

There's no sufficient evidence to reject the claim that the national board is better than the store board

Step-by-step explanation:

There are some missing information in the question you posted.

They are: sample size, number of success and significance level.

The values of these are given below.

Given that

n = Sample Size = 35

x = Number of Success = 8

∝ = Significance level = 5% = 0.05

First we need to state the null and alternative hypothesis.

Given that proportion is more than 50%.

The claim is either null hypothesis or the alternative hypothesis.

The null hypothesis states that; the proportion is equal to the claimed value while that alternative hypothesis is the opposite of the null hypothesis.

See attachment for more explanation

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step-by-step explanation:

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.