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3 years ago

10

The standard tip in a restaurant is 15% of the bill before tax. Many people in California find the tip by doubling the sales tax

, which is 8.25%. By how many cents does this exceed the standard tip on a bill of 60% before tax?

1 answer:

cricket20 [7]3 years ago

3 0

To answer this you could do a couple things. 1. Actually calculate both tips and then subtract them. Here is the math ( assuming it is $60, not 60% that you mean). a. 0.15 x 60 = $9. b. 0.0825 x 2 x 60=$9.90. c. 9.90-9.00= $0.90 difference.

The other strategy would be to find the difference on the percents and then multiply by $60. a. 8.25%x2=16.5%-15%. Difference of 1.5%. b. 0.015 x $60=$0.90.

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Answer:

$t=\frac{669-634}{\frac{732}{\sqrt{1700}}}=1.971$

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Step-by-step explanation:

Data given and notation

$\bar X=669$ represent the sample mean

$s=732$ represent the sample standard deviation

$n=1700$ sample size

$\mu_o =68$ represent the value that we want to test

$\alpha=0.$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is different from 634, the system of hypothesis would be:

Null hypothesis: $\mu = 634$

Alternative hypothesis: $\mu \neq 634$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{669-634}{\frac{732}{\sqrt{1700}}}=1.971$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=1700-1=1699$

Since is a two sided test the p value would be:

$p_v =2*P(t_{(1699)}>1.971)=0.049$

Conclusion

If we compare the p value and the significance level given $\alpha=0.1$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the true mean is different from 634 at 10% of signficance.

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Step-by-step explanation:

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Sherman has $22 to spend on pet toys.

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Answer:

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Step-by-step explanation:

Previous concepts

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The probability mass function for the Binomial distribution is given as:

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Let X the random variable of interest, on this case we now that:

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For this case we can use the probability mass function and we got:

$P(X= 5) = (15C5) (0.25)^{5} (1-0.25)^{15-5}= 0.165$

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3 years ago