Find the function value of f(4) if f(x)=3(x)-2

A company surveyed 2400 men where 1248 of the men identified themselves as the primary grocery shopper in their household. a) E

polet [3.4K]

Answer:

a) With a confidence level of 98%, the percentage of all males who identify themselves as the primary grocery shopper are between 0.4962 and 0.5438.

b) The lower limit of the confidence interval is higher that 0.43, so if he conduct a hypothesis test, he will find that the data shows evidence to said that the fraction is higher than 43%.

c) $\alpha =1-0.98=0.02$

Step-by-step explanation:

If np' and n(1-p') are higher than 5, a confidence interval for the proportion is calculated as:

$p'-z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }\leq p\leq p'+z_{\alpha/2}\sqrt{\frac{p'(1-p')}{n} }$

Where p' is the proportion of the sample, n is the size of the sample, p is the proportion of the population and $z_{\alpha/2}$ is the z-value that let a probability of $\alpha/2$ on the right tail.

Then, a 98% confidence interval for the percentage of all males who identify themselves as the primary grocery shopper can be calculated replacing p' by 0.52, n by 2400, $\alpha$ by 0.02 and $z_{\alpha/2}$ by 2.33

Where p' and $\alpha$ are calculated as:

$p' = \frac{1248}{2400}=0.52\\\alpha =1-0.98=0.02$

So, replacing the values we get:

$0.52-2.33\sqrt{\frac{0.52(1-0.52)}{2400} }\leq p\leq 0.52+2.33\sqrt{\frac{0.52(1-0.52)}{2400} }\\0.52-0.0238\leq p\leq 0.52+0.0238\\0.4962\leq p\leq 0.5438$

With a confidence level of 98%, the percentage of all males who identify themselves as the primary grocery shopper are between 0.4962 and 0.5438.

The lower limit of the confidence interval is higher that 0.43, so if he conduct a hypothesis test, he will find that the data shows evidence to said that the fraction is higher than 43%.

Finally, the level of significance is the probability to reject the null hypothesis given that the null hypothesis is true. It is also the complement of the level of confidence. So, if we create a 98% confidence interval, the level of confidence $1-\alpha$ is equal to 98%

It means the the level of significance $\alpha$ is:

$\alpha =1-0.98=0.02$

4 0

3 years ago

A teacher has 100 chairs to arrange for an assembly into equal rows Write one way the chairs could be arranged Include the numbe

tiny-mole [99]

That's easy if there is 100 chairs there would be 10 rows with ten chairs in each row

3 0

3 years ago

Read 2 more answers

4.) Order the following decimals from greatest to least. 15.9 9.5 1.95 9.15 1.59

olya-2409 [2.1K]

1.59, 1.95, 9.15, 9.5, 15.9

3 0

3 years ago

Find three consecutive integers such that three times the first added to the last is 22

Finger [1]

Consetive integers are 1 apart
they are
x,x+1,x+2

3 times the first added to the last is 22
3x+x+2=22
combine like terms
4x+2=22
minus 2 both sides
4x=20
divide both sides by 4
x=5
x+1=6
x+2=7

the numbers are 5,6,7

4 0

3 years ago

A 14-ounce box of cereal sells for $2.10. What is the unit rate?

Ahat [919]

Answer:

The unit rate is equal to $0.15\frac{\$}{ounce}$