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harina [27]
3 years ago
7

Which expression should you simplify to find the 90% confidence interval,

Mathematics
1 answer:
bogdanovich [222]3 years ago
5 0

Answer:

0.45 - 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.2870.45 + 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.613

we can conclude at 95% of confidence that the true proportion of interest for this case is between 0.287 and 0.613

Step-by-step explanation:

The estimated proportion of interest is \hat p=0.45

We need to find a critical value for the confidence interval using the normla standard distributon. For this case we have 95% of confidence, then the significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025.

And the critical value is:z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The confidence interval for the true population proportion is interest is given by this formula:  

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}

Replacing the values provided we got:

0.45 - 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.287\\\\0.45 + 1.96\sqrt{\frac{0.45(1-0.45)}{36}}=0.613

And we can conclude at 95% of confidence that the true proportion of interest for this case is between 0.287 and 0.613

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What are all of the real roots of the following polynomial?<br> f(x) = x4 - 15x2 + 10x + 24
Ber [7]

Answer:

x = −1 ,2 , 3 , − 4

Step-by-step explanation:

7 0
3 years ago
An angle has a measure of 150° and a terminal side that intercepts the unit circle at (x,y). What are the values of x and y?
V125BC [204]

Answer:

x = -√3 /2

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Step-by-step explanation:

x = cos 150°= -√3 /2

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4 0
3 years ago
Jenny's mom is 36 years old. If Jenny's great-grandmother is 90 years old, what percent of Jenny's mother's age is Jenny's great
Serjik [45]

Answer:

The age of Jenny's mom is 40 % of age of Jenny's great-grandmother.  (Input: 40)

Step-by-step explanation:

The percentage needed is calculated by the following expression:

x = \frac{n_{M}}{n_{G}}\times 100\,\%

Where:

x - Percentage of Jenny's mother with respect to Jenny's great-grandmother, measured in percentage.

n_{M} - Age of Jenny's mother, measured in years.

n_{G} - Age of Jenny's great-grandmother, measured in years.

If we know that n_{M} = 36\,yr and n_{G} = 90\,yr, the percentage is:

x = \frac{36\,yr}{90\,yr} \times 100\,\%

x = 40\,\%

The age of Jenny's mom is 40 % of age of Jenny's great-grandmother.

3 0
3 years ago
A swimming pool is being drained so it can be cleaned. The amount of water in the pool is changing according to the función f(t)
TiliK225 [7]

Answer:

0 ≤ t ≤ 5.

Step-by-step explanation:

In the function f(t), t is the independent variable. The domain of f is the set of all values of t that this function can accept.

In this case, f(t) is defined in a real-life context. Hence, consider the real-life constraints on the two variables. Both time and volume should be non-negative. In other words,

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  • f(t) \ge 0.

The first condition is an inequality about t, which is indeed the independent variable.

However, the second condition is about f, the dependent variable of this function. It has to be rewritten as a condition about t.

\begin{aligned} f(t) &\ge 0 &&\text{Assumption} \cr 80000 - 16000\, t& \ge 0 && \text{Definition of} ~ f \cr 80000 & \ge 16000\, t && \begin{aligned}&\text{Add $16000\, t$} \\[-0.5em] & \text{to both sides of the inequality}\end{aligned} \cr 5 &\ge t &&\begin{aligned}&\text{Divide both sides of} \\[-0.5em] & \text{the inequality by $16000$}\end{aligned} \cr t &\le 5 && \text{Flip the inequality}\end{aligned}.

Hence, t ≤ 5.

Combine the two inequalities to obtain the domain:

0 ≤ t ≤ 5.

6 0
2 years ago
Which is equal to 6^-8/6^-2 A. 616 B. 64 C. 6−6 D. 6−10
rjkz [21]
6-6.
6^-8/6^-2 becomes 6^-8(6^2) which is 6^-8+2=6^-6
4 0
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