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Exam 6: Introduction to Inference

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Question 41

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A study was conducted on the reaction time of female subjects over the age of 50 to a particular light stimulus using a specific type of red light.A random sample of 45 female subjects from this age group in the population was selected and the subject's reaction time (in seconds) determined.Based on the test data,the 99% confidence interval estimate for  was determined to be (0.66,0.78) .From this interval we can conclude that

A) this interval contains the sample mean with probability 0.99.
B) this interval has a probability of 0.99 of enclosing the true mean .
C) this interval,in the long run,will contain the true mean  99% of the time.
D) we have 99% confidence in this interval because,in repeated sampling from the population,the method used to determine such confidence intervals will produce intervals 99% of which will contain .
E) we have 99% confidence that this interval contains  because,if we repeated testing over and over again,99% of the time this interval will contain .

F) B) and E)
G) A) and B)

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Question 42

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The lifetime (in hours) of a 60-watt light bulb is a random variable that has a Normal distribution with  = 30 hours.A random sample of 25 bulbs put on test produced a sample mean lifetime of = 1038.Construct a 92% confidence interval estimate for the mean lifetime .If it were desired to cut the confidence interval to half its length while keeping the same 92% level,what size sample would be required to achieve this?

A) 50
B) 13
C) 75
D) 100
E) 41

F) C) and E)
G) B) and D)

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Question 43

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Suppose a study was done to determine if the average amount of sleep that students get the day before an exam is less than 6 hours.An SRS of 100 students from a university was taken and a mean of 5.5 hours was computed from the sample.The figure below provides the results of the analysis. What is the alternative hypothesis?

What is needed to compute a margin of error?

The null hypothesis is a statement about the ________.

In the last mayoral election in a large city,47% of the adults over the age of 65 voted Republican.A researcher wishes to determine if the proportion of adults over the age of 65 in the city who plan to vote Republican in the next mayoral election has changed.Let p represent the proportion of the population of all adults over the age of 65 in the city that plan to vote Republican in the next mayoral election.In terms of p,the researcher should test which of the following null and alternative hypotheses?

The breaking strength of yarn used in the manufacture of woven carpet material is Normally distributed with  = 2.4 psi.A random sample of 16 specimens of yarn from a production run was measured for breaking strength,and based on the mean of the sample ,a confidence interval was found to be (128.7,131.3) .What is the confidence level,C,of this interval?

Confidence intervals are useful when trying to estimate _______.

Suppose a study was done to determine if the average amount of sleep that students get the day before an exam is less than 6 hours.An SRS of 100 students from a university was taken and a mean of 5.5 hours was computed from the sample.The figure below provides the results of the analysis. Suppose the alternative hypothesis is H_a:   6.Would the null hypothesis be rejected at the .01 level?

An agricultural researcher plants 25 plots with a new variety of yellow corn.Assume that the yield per acre for the new variety of yellow corn follows a Normal distribution with an unknown mean of  and a standard deviation of  = 10 bushels per acre. Which of the following would produce a confidence interval with a smaller margin of error than the 90% confidence interval?

In a test of statistical hypotheses,what does the P-value tell us?

Suppose we are interested in determining the average amount of money students spend on car maintenance every year.If we obtained 120 SRS of size 100 and constructed an 80% confidence interval for each SRS,we would expect ______ of the confidence intervals to contain the true population mean.

Battery packs in radio-controlled racing cars need to be able to last pretty long.The distribution of the lifetimes of battery packs made by Lectric Co.is slightly left skewed.Assume that the standard deviation of the lifetime distribution is  = 2.5 hours.A simple random sample of 75 battery packs results in a mean of = 29.6 hours.What is a 90% confidence interval for ,the true average lifetime of the battery packs made by Lectric Co.?

Suppose a study was done to determine if the average amount of sleep that students get the day before an exam is less than 6 hours.An SRS of 100 students from a university was taken and a mean of 5.5 hours was computed from the sample.The figure below provides the results of the analysis. Suppose the alternative hypothesis is H_a:   6.Would the null hypothesis be rejected at the .05 level?

The null and alternative hypotheses are stated in terms of the statistics from the random sample.

The results obtained from a test of significance can always be trusted as long as the data collection methods are correct.

Typically,the null hypothesis in a test of significance is a statement of "no difference" in the true means.

Suppose a 99% confidence interval for the mean weight of high school girls (in pounds) is calculated as (102.3,106.5) .If we had measured the weights of each of the girls in kilograms (2.2 pounds = 1 kilogram) ,then the confidence interval for the mean weight of high school girls in kilograms would have been

You perform 2000 significance tests using a significance level,,of 0.10.Assume that all of the null hypotheses for the 2000 significance tests are true.How many of the 2000 significance tests would be statistically significant?

The basic form of a confidence interval is __________________.