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Review for test 2

By Leroy Simpson,2014-03-31 21:33
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Review for test 2

Review for test 2

Chapter 6

    1 A random sample of n = 800 observations is selected from a population with

    mean 100 and variance =100

    ;xxa) What are the values of and . (100,.354)

    xb) What are the largest and smallest value of that you would expect to

    see? (101.062 and 98.938)

    xc) Will the sampling distribution of be approximately normal?

    Explain(Central Limit theorem)

     (Section 6.1)

    2 A random sample of size 400 is taken from a population having mean zero

    and standard deviation 2400. In what interval of real numbers should we

    expect to see 75% of the means of any samples of size 400? (-240.240)

    3 If x is normally distributed with a mean of 30 and a standard deviation of 12,

    find P(30 < x < 45.6). (z= 1.3, 0.403)

    4 The score for a test has a mean of 250 and variance of 2025

     If the test was given to a random of 50 people, what is the probability that

    these 50 people would have a mean test score

     a) Larger than 265 (Ans:0.009)

     b) Between 240 and 250 (Ans:0.442)

    5 A random sample of n = 40 observations is selected from a population with

    mean 2.5 and standard deviation of 1.5, find each of the following:

     Ans (.017) P(x3)

    P(x3) Ans (.983)

    Chapter 7

    1)

    A mirror maker claims his best product has an average lifespan of exactly 20 years. A skeptical quality control specialist asks for evidence (data) that might be used to evaluate this claim. The quality control specialist was provided data collected from a random sample of 50 people who used the product. Using the data, an average product lifespan of 15 years and a standard deviation of 4 years was calculated.

    a) Does the data indicate, at the significance level 0.01, that true mean

    lifespan of the product exceeds that of the claimed average lifespan of

    20 years? State the conditions (-8.83)

    b) Select the 99% confidence interval for the true mean lifespan of this

    product (13.54, 16.46)

    2) An important problem in industry is shipment damage. A pottery producing

    company ships its product by truck and determines that it cannot meet its

    profit expectations if, on average, the number of damaged items per

    truckload is greater than 12. A random sample of 12 departing truckloads is

    selected at the delivery point and the average number of damaged items per

    truckload is calculated to be 14.3 with a calculated sample variance of .49.

    Perform the appropriate hypothesis test, at significance level 0.01, to

    determine whether profit expectations cannot be met. ? State the conditions

     (t= )

    3) An important problem in industry is shipment damage. An electronics

    distribution company ships its product by truck and determines that it can

    meet its profit expectations if, on average, the number of damaged items per

    truckload is fewer than 10. A random sample of 19 departing truckloads is

    selected at the delivery point and the average number of damaged items per

    truckload is calculated to be 9.4 with a calculated sample variance of .49.

    Select a 99% confidence interval for the true mean of damaged items.

    (8.94 to 9.86)

    4) It has been observed that some persons who suffer colitis are diagnosed with

    it again within one year of the first episode. This is due, in part, to damage

    from the first episode. In order to examine the percentage of the persons who

    suffer colitis a second time, a random sample of 1000 people who suffered

    colitis was collected. It was observed that 15 of them again suffered colitis

    within one year. Conduct a hypothesis test to determine, at the significance

    level 0.05, whether there is reason to believe that the population percentage

    of those who suffer a second episode is less than 3%.? State the conditions

     (z= -2.78 reject null)

    5) It has been observed that some persons who suffer from common colds are diagnosed with it again within one year of the first episode. This is due, in part, to damage from the first episode. In order to examine the percentage of the persons who suffer from common colds a second time, a random sample of 1200 people who suffered from common colds was collected and it was observed that 17 of them again suffered from common colds within one year. Select a 95% confidence interval for the true proportion of those who suffer a second episode. Use the appropriate table in your book.

    (0.0074 to 0.0208)

    6) What is the minimum number of employees that should be sampled by the Exxon Corporation if it wishes to estimate the true mean number of years to retirement of its employees to within one month of the true mean and with 90% confidence if the range of the data is 7 years? Use the appropriate table in your book. ( (n= 1201)

    7) Television viewers often express doubts about the validity of certain commercials. In a attempt to answer their critics, a large advertiser wants to estimate the true proportion of consumers who believe what is shown in commercials. Preliminary studies indicate that about 40% of those surveyed believe what is shown in commercials. What is the minimum number of consumers that should be sampled by the advertiser to be 95% confident that their estimate will fall within 2% of the true population proportion? Use the appropriate table in your book. (n= 2304)

    8) An oil company is interested in estimating the true proportion of female truck drivers based in five southern states. A statistician hired by the oil company must determine the sample size needed in order to make the estimate accurate to within 2% of the true proportion with 95% confidence. What is the minimum number of truck drivers that the statistician should sample in these southern states in order to achieve the desired accuracy? Use the appropriate table in your book. (n=2400)

    9) The variance, over the past 5 years, of the widths (in inches) of a particular manufactured product has been 100. However, recent changes have given rise to the suspicion that this may no longer be the case. A recent sample of 26 such product widths had a calculated sample standard deviation of 8 and mean of 11.3. Does the sample provide sufficient evidence, at the significance level 0.01, to conclude that the variance is now smaller than that of the variance over the past 5 years? State the Conditions. Chi square = 16, insufficient evidence)

    10) The variance, over the past 7 years, of the lengths (in inches) of a particular manufactured product has been 80. However, recent changes have given rise to the suspicion that this may no longer be the case. A recent sample of 15 such product lengths had a calculated sample standard deviation of 8 and mean of 9.4. Select the 95% confidence for the true variance of the product lengths. Use the appropriate table in your book. ( 34.33 to 159.15)

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