\fTABLE A.7 Critical values of t Please use this Upper tail area (shaded) table to find the t 0 terit values Upper tail areas df 1.05 1.025 101 3.078 6.314 12.706 31.821 53.657 318.309 1.886 2.920 4.303 6.965 9.925 22.327 1.638 2.353 3.182 4.541 5.841 10.215 1.533 2.132 2.776 3.747 4.604 7.173 1.476 2.015 2.571 3.365 4.032 5.893 1.440 1.943 2.447 3.143 3.707 5.208 1.415 1.895 2.365 2.998 3.499 4.785 GAGNE SOONO DAWN- 1.397 1.860 2.306 2.896 3.355 4.501 1.383 1.833 2.262 2.821 3.250 4.297 1.372 1.812 2.228 2.764 3.169 4.144 1.363 1.796 2.201 2.718 3.106 4.025 1.356 1.782 2.179 2.681 3.055 3.930 1.350 1.771 2.160 2.650 3.012 3.852 1.345 1.761 2.145 2.624 2.977 3.787 1.341 1.753 2.131 2.602 2.947 3.733 16 1.337 1.746 2.120 2.583 2.921 3.686 17 1.333 1.740 2. 110 2.567 2.898 3.646 18 1.330 1.734 2. 101 2.552 2.878 3.610 19 1.328 1.729 2.093 2.539 2.861 3.579 20 1.325 1.725 2.086 2.528 2.845 3.552 21 1.323 1.721 2.080 2.518 2.831 3.527 22 1.321 1.717 2.074 2.508 2.819 3.505 23 1.319 1.714 2.069 2.500 2.807 3.485 24 1.318 1.711 2.064 2.492 2.797 3.467 25 1.316 1.708 2.060 2.485 2.787 3.450 1.315 1.706 2.056 2.479 2.779 3.435 1.314 1.703 2.052 2.473 2.771 3.421 28 1.313 1.701 2.048 2.467 2.763 3.408 29 1.311 1.699 2.045 2.462 2.756 3.396 30 1.310 1.697 2.042 2.457 2.750 3.385 31 1.309 1.696 2.040 2.453 2.744 3.375 1.309 1.694 2.037 2.449 2.738 3.365 33 1.308 1.692 2.035 2.445 2.733 3.356 34 1.307 1.691 2.032 2.441 2.728 3.348 35 1.306 1.690 2.030 2.438 2.724 3.340 36 1.306 1.688 2.028 2.434 2.719 3.333 1.305 1.687 2.026 2.431 2.715 3.326 38 1.304 1.686 2.024 2.429 2.712 3.319 39 1.304 1.685 2.023 2.426 2.708 3.313 40 1.303 1.684 2.021 2.423 2.704 3.307 41 1.303 1.683 2.020 2.421 2.701 3.301 42 1.302 1.682 2.018 2.418 2.698 3.296 43 1.302 1.681 2.017 2.416 2.695 3.291 44 1.301 1.680 2.015 2.414 2.692 3.286 45 1.30 1.679 2.014 2.412 2.690 3.281 46 1.300 1.679 2.013 2.410 2.687 3.277 47 1.300 1.678 2.012 2.408 2.685 3.273 48 1.299 1.677 2.011 2.407 2.682 3.269 1.299 1.677 2.010 2.405 2.680 3.265 50 1.299 1.676 2.009 2.403 2.678 3.261\fQUESTION 1 Strategic business planning is required forthe successful transfer ofcontrol between generations in familyowned companies. However, a survey of 360 privately held family firms whose annual turnover exceeded one million dollars it was found that 91 had no strategic business plan. Assuming that simple random sampling was employed to determine the sample for the surveyr estimate with 95% confidence the proportion offamin-owned companies operating without strategic business plans. Give the upper limit only and report your answer correct to three decimal places. QUESTION 2 ANZ Bank's Wealth Management Division conducted a survey of the value ofthe new business created overthe last month in millions of dollars. From 20 responses, the mean and standard deviation were found to be $8.365 and $0.922 million respectively. Assuming the data were collected through a random sample and that the value of new business is approximately normally distributed, calculate a 98% confidence interval estimate of the average value of new business per month in millions of dollars. State only the upper bound correct to three decimal places. QUESTION 5 A sales consultant for Herron Pharmaceuticals wished to confirm that their packet of 24 paracetamol tablets was cheaper at the retail level than their rival product. The sales consultant collected price data from two independent samples, of size 27 for Herron and 18 for the rival company. These yielded an average and variance forthe retail price of Herron's product of 386 cents and 59 cents squared respectively, and 419 cents and 50 cents squared for the rival. Under the usual assumptions, determine a 95% confidence interval for the price difference [use Herron minus rival) stating only the upper limit of the interval in cents (round to the nearest whole number). QUESTION 6 People in the aerospace industry conducted a pilot study to determine the relationship between the weight and cost of a major object being sent into space. The results of the pilot study are contained in datafile SP13.53, contained in a folder under the CML Quizzes tab. Determine the number of observations needed to be 91% confident that the estimate of the average cost is within $10 ofthe overall mean cost. Note: Assume that the pilot study standard deviation is a good estimate of the population standard deviation, that an appropriate value from the Ztable can be used, and that hand calculations are used to find the answer (Le. do not use Kaddstat}. Hint: in Excel, use Data > Data Analysis > Descriptive Statistics, to find the sample Standard deVlatlon' This question needs data from excel, i've already upload the screenshoot of excel, please see it on the next page, thanks a lot 111 QUESTION 3 Consider the following statements concerning confidence interval estimates: A. If the confidence level is increased, then the sample size would also need to be increased, if the precision (width of confidence interval) is to be maintained. B. For a given level of confidence, sample size and standard deviation, the width of a confidence interval for the mean will be the same regardless of whether the standard deviation is a population or sample measure. C. Where no prior information is available concerning an estimate of the true population proportion, a conservative estimate of the sample size required to obtain a confidence interval with given levels of confidence and precision can be determined by letting the proportion equal 1/2. O only A is true O only A and B are true O only A and C are true O only B and C are true O A, B and C are true QUESTION 4 Courier Express wished to determine the average weight of parcels carried by its Brisbane operations. On the basis of historical data, the company was aware that the weight of parcels could be approximated by a normal distribution with a variance of 0.437 kilograms squared. Last month, it weighed a random sample of 22 parcels and found the average weight was 2.236 kg. Determine a 95% confidence interval for the average weight of parcels carried by Courier Express. State the upper limit of the interval only, giving your answer to two decimal places.QUESTION 7 An interval estimate for the average distance car tyres lasted during their "lifetime" was reported to be 32468 km to 37224 km. This interval estimate was based on a sample of48 tyres. The variance ofthe lifetime was determined from previous studies to be 44582179 km squared. What level of confidence can be attributed to this interval estimate? State your answer as a percentage. correct to the nearest whole number. QUESTION 8 Suppose that the duration of trouble-free operation of a new vacuum cleaner is normally distributed with a mean of 72 weeks and variance of 144 weeks2. The research department randomly selects 25 customers who bought these vacuum cleaners and records duration (in weeks) of trouble-tree operation. The standard error of the sample mean is weeks (1 decimal place}. The probability that the average duration of trouble-free operation time is between T5 weeks and 78 weeks is (4 decimal places)