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valentinak56 [21]
3 years ago
6

A survey was conducted that asked 1003 people how many books they had read in the past year. Results indicated that x overbar eq

uals 12.8 books and sequels 16.6 books. Construct a 99​% confidence interval for the mean number of books people read. Interpret the interval.
Mathematics
1 answer:
Sergio [31]3 years ago
3 0

Answer:

The 99% confidence interval would be given (11.448;14.152).

Step-by-step explanation:

1) Important concepts and notation

A confidence interval for a mean "gives us a range of plausible values for the population mean. If a confidence interval does not include a particular value, we can say that it is not likely that the particular value is the true population mean"

s=16.6 represent the sample deviation

\bar X=12.8 represent the sample mean

n =1003 is the sample size selected

Confidence =99% or 0.99

\alpha=1-0.99=0.01 represent the significance level.

2) Solution to the problem

The confidence interval for the mean would be given by this formula

\bar X \pm z_{\alpha/2} \frac{s}{\sqrt{n}}

We can use a z quantile instead of t since the sample size is large enough.

For the 99% confidence interval the value of \alpha=1-0.99=0.01 and \alpha/2=0.005, with that value we can find the quantile required for the interval in the normal standard distribution.

z_{\alpha/2}=2.58

And replacing into the confidence interval formula we got:

12.8 - 2.58 \frac{16.6}{\sqrt{1003}}=11.448

12.8 + 2.58 \frac{16.6}{\sqrt{1003}} =14.152

And the 99% confidence interval would be given (11.448;14.152).

We are confident that about 11 to 14 are the number of books that the people had read on the last year on average, at 1% of significance.

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Answer:

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Step-by-step explanation:

Distribute:

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Step-by-step explanation:

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Answer:

Larger sample size gives less std error and hence test statistic is larger.

Step-by-step explanation:

Given that a newspaper  is conducting a statewide survey concerning the race for governor. The newspaper will take a simple random sample of n registered voters and determine X = the number of voters that will vote for the Democratic candidate. Is there evidence that a clear majority of the population will vote for the Democratic candidate

Group        I   II

Success    640 64

Total   1200 120

p 0.533333333 0.533333333

q 0.466666667 0.466666667

se 0.014401646 0.045542003

p diff 0.033333333 0.033333333

Z 2.314550249 0.731925055

p      0.01           0.233

we find that though p is the same, std error is very small for larger sample size thus making z statistic much bigger.  So we get p value less than 0.05 whereas for 120 sample size, std error is large so Z statistic is small thus making p value to accept null hypothesis

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A study of 35 golfers showed that their average score on a particular course was 92. The sample standard deviation was 5. We wan
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Answer:

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Step-by-step explanation:

We have a sample of size n = 35, \bar{x} = 92 and s = 5. As we want to construct a 95% confidence interval to estimate the value of the true population mean \mu, we should use the pivotal quantity given by T = \frac{\bar{X}-\mu}{S/\sqrt{n}} which comes from the t distribution with n - 1 = 35 - 1 = 34 degrees of freedom. Besides we should use the t-value t_{\alpha/2} = t_{0.05/2} = t_{0.025} = 2.0322, i.e., regarding the t-distribution with 34 degrees of freedom, we have an area of 0.025 above 2.0322 and below the probability density function. The rationale behind this is that P(-2.0322\leq T\leq 2.0322) = 0.95 because of the simmetry of the t distribution.

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