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goldfiish [28.3K]
2 years ago
13

Evaluate the geometric series . 254 255 508 510

Mathematics
2 answers:
Svetach [21]2 years ago
5 0
A1<span> is the first term in the </span>sequence<span>. To find the explicit </span>formula, you will need to be given the first term and use the value in the formula<span>. r is the common ratio for </span>the geometric sequence<span>. You will be given this value or be given information to compute it.</span>
mihalych1998 [28]2 years ago
3 0

Answer with explanation:

The given geometric series is : 254, 255, 508, 510,....

→If you will look at the first term and third term , it is

 254, 254 × 2,

So,First Half of the series will be as follows :

254×1, 254×2, 254×3,254×4,254×5........

→And if you will look at the second term and fourth term, it is as follows:

255, 255×2,

So,Second Half of the series will proceed as follows:

  255×1, 255×2, 255×3, 255×4,.........

⇒So, the whole series will be as follows:

254, 255, 254×2,255×2,254×3,255×3,254×4,255×4,....

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Answer:

Yes, since the test statistic value is greater than the critical value.

Step-by-step explanation:

Data given and notation

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\bar X_{2}=340000 represent the mean for the freeway restaurant

s_{1}=50000 represent the sample standard deviation for downtown

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We need to conduct a hypothesis in order to check if the true mean of revenue for downtown is higher than for freeway restaurant, the system of hypothesis would be:

Null hypothesis:\mu_{1}\leq \mu_{2}

Alternative hypothesis:\mu_{1} > \mu_{2}

Since we don't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:

t=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}} (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Determine the critical value.

Based on the significance level\alpha=0.05 and \alpha/2=0.025 we can find the critical values from the t distribution dith degrees of freedom df=36+36-2=55+88-2=70, we are looking for values that accumulates 0.025 of the area on the right tail on the t distribution.

For this case the value is t_{1-\alpha/2}=1.66

Calculate the value of the test statistic for this hypothesis testing.

Since we have all the values we can replace in formula (1) like this:

t=\frac{360000-340000}{\sqrt{\frac{50000^2}{36}+\frac{40000^2}{36}}}}=1.874

What is the p-value for this hypothesis test?

Since is a right tailed test the p value would be:

p_v =P(t_{70}>1.874)=0.033

Based on the p-value, what is your conclusion?

Comparing the p value with the significance level given \alpha=0.05 we see that p_v so we can conclude that we reject the null hypothesis, and the true mean for the downtown revenue restaurant seems higher than the true mean revenue for the freeway restaurant.

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