A manufacturer of potato chips would like to know whether its bag filling machine works correctly at the 443 gram setting. It is believed that the machine is underfilling the bags. A 15 bag sample had a mean of 434 grams with a standard deviation of 17. A level of significance of 0.1 will be used. Assume the population distribution is approximately normal. Determine the decision rule for rejecting the null hypothesis. Round your answer to three decimal places.

Null hypothesis

Alternative hypothesis

t = - 2.05

Degree of freedom df = 14

P-value = 0.0298

Decision rule: To reject   if significance level ∝  is greater than P-value.

Conclusion: We reject at the level of significance ∝ = 0.1, thus there is sufficient evidence to conclude that the machine is underfilling the bags.

Step-by-step explanation:

Given that:

Population mean = 443

Sample size n = 15

Sample mean = 434

standard deviation = 17

Level of significance ∝ = 0.01

The null and the alternative hypothesis can be computed as:

Null hypothesis

Alternative hypothesis

The t-test statistics can be computed as :

t = - 2.05

Degree of freedom df = n - 1

Degree of freedom df = 15 - 1

Degree of freedom df = 14

From t distribution table; from the area in the lower tail to the left of t = -2.05 and for  the degree of freedom df = 14, it is given by 0.0298

Thus, P-value = 0.0298

Decision rule: To reject   if significance level ∝  is greater than P-value.

Conclusion: We reject at the level of significance ∝ = 0.1, thus there is sufficient evidence to conclude that the machine is underfilling the bags.

l.ln.lln.k.nkl

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4