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# Qmet 252 Essay

A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed, a sample of nine boxes of cake mix gave these shelf lives (in days): 215, 217, 218, 219, 216, 217, 217, 218 and 218. At the 0. 025 level, has the shelf life of the cake mix increased? Choose one answer. ||a. No, because computed t lies in the region of acceptance. | | ||b. Yes, because computed t is less than the critical value. | | ||c.

Yes, because computed t is greater than the critical value. | | ||d. No, because 217. 24 is quite close to 216. | | Population standard deviation unknown, we need to use t test. Using data analysis, we can easily get the sample mean 217. 222 and sample standard deviation 1. 202. Ho: u 216 Reject Ho if t > 2. 306 (one-tailed test with a = 0. 025 and df = 8) t = (217. 222 – 216) / (1. 202/sqrt(9)) = 3. 05 Reject Ho. The shelf life of the cake mix has increased. Correct Marks for this submission: 2/2.

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Question 2 Marks: 1 If ? = 0. 05 for a two-tailed test, how large is the acceptance area? Choose one answer. ||a. 0. 025 | | ||b. 0. 975 | | ||c. 0. 05 | | ||d. 0. 95 | | Incorrect Marks for this submission: 0/1. Question 3 Marks: 1 A random sample of size 15 is selected from a normal population. The population standard deviation is unknown. Assume that a two-tailed test at the 0. 10 significance level is to be used. For what value of t will the null hypothesis not be rejected? Choose one answer. ||a. To the left of -1. 345 or to the right of 1. 45 | | ||b. To the left of -1. 645 or to the right of 1. 645 | | ||c. To the left of -1. 282 or to the right of 1. 282 | | ||d. Between -1. 761 and 1. 761 | | n=15 => df = 15-1=14 a = 0. 10 (two-tailed test) Decision rule: rejection Ho if calculated t > 1. 761 or t < -1. 761; or in other words, we will not reject the null hypothesis if the value of t falls between -1. 761 and 1. 761. Correct Marks for this submission: 1/1. Question 4

Marks: 2 A manufacturer of stereo equipment introduces new models in the fall. Retail dealers are surveyed immediately after the Christmas selling season regarding their stock on hand of each piece of equipment. It has been discovered that unless 40% of the new equipment ordered by the retailers in the fall had been sold by Christmas, immediate production cutbacks are needed. The manufacturer has found that contacting all of the dealers after Christmas by mail is frustrating as many of them never respond. This year 80 dealers were selected at random and telephoned regarding a new receiver.

It was discovered that 38% of those receivers had been sold. Since 38% is less than 40%, does this mean that immediate production cutbacks are needed or can this difference of 2 percentage points be attributed to sampling? Test at the 0. 05 level. Choose one answer. ||a. Cut back production | | ||b. Cannot determine based on information given | | ||c. None of these | | ||d. Do not cut back production | |

It is a testing concerning proportions. Ho: ? >= 0. 4 H1: ? < 0. 4 (reflection of the inquiry – immediate production cutbacks are needed if less than 40% of the new equipment ordered by the retailers in the fall had been sold by Christmas). Decision rule: reject Ho if z < -1. 65 Z = (0. 38 – 0. 4)/sqrt(0. 4*(1-0. 4)/80) = -0. 37 Do not reject Ho. The manufacturer will not cut back production. Correct Marks for this submission: 2/2. Question 5 Marks: 1 A machine is set to fill the small size packages of M&M candies with 56 candies per bag. A sample revealed: 3 bags of 56, 2 bags of 57, 1 bag of 55, and 2 bags of 58.

How many degrees of freedom are there? Choose one answer. ||a. 7 | | ||b. 9 | | ||c. 6 | | ||d. 8 | | ||e. 1 | | Total number of bags = 3+2+1+2=8 df = 8-1=7 Incorrect Marks for this submission: 0/1. Question 6 Marks: 1 What value does the null hypothesis make a claim about? Choose one answer. ||a. Population parameter | | ||b. Sample mean | | ||c. Sample statistic | | ||d. Type II error | | Correct

Marks for this submission: 1/1. Question 7 Marks: 1 If ? = 0. 05, what is the probability of making a Type I error? Choose one answer. ||a. 20/20 | | ||b. 19/20 | | ||c. 1/20 | | ||d. 0 | | Correct Marks for this submission: 1/1. Question 8 Marks: 1 What is the level of significance? Choose one answer. ||a. Beta error | | ||b. Probability of a Type II error | | ||c. Probability of a Type I error | | ||d. z-value of 1. 6 | | Correct Marks for this submission: 1/1. Question 9 Marks: 1 What is the critical value for a one-tailed hypothesis test in which a null hypothesis is tested at the 5% level of significance based on a sample size of 25? Choose one answer. ||a. 1. 711 | | ||b. 2. 064 | | ||c. 1. 708 | | ||d. 2. 06 | | df = 25-1=24 a = 0. 05 one-tailed test, the corresponding value of t is 1. 711 Correct Marks for this submission: 1/1. Question 10 Marks: 1 In hypothesis testing, what is the level of significance?

Choose one answer. ||a. Value between 0 and 1 | | ||b. Risk of rejecting the null hypothesis when it is true | | ||c. Symbolized by the Greek letter “a” | | ||d. All of the others are true | | ||e. Selected before a decision rule can be formulated | | Incorrect Marks for this submission: 0/1. Question 11 Marks: 1

For a one-tailed hypothesis test, the critical z-value of the test statistic is -2. 33. Which of the following is true about the hypothesis test? Choose one answer. ||a. a = 0. 01 for an upper-tailed test | | ||b. a = 0. 01 for a lower-tailed test | | ||c. a = 0. 05 for a lower-tailed test | | ||d. a = 0. 05 for an upper-tailed test | | The absolute value of -2. 33 gives an area under the normal curve of 0. 4901. It’s one-tailed test, thus a = 0. 5 – 0. 4901 = 0. 0099 = 0. 01.

The critical z-value is -2. 33, thus in the lower or left tail. Correct Marks for this submission: 1/1. Question 12 Marks: 1 What are the two critical values for a two-tailed test with a 0. 01 level of significance when n is large and the population standard deviation is known? Choose one answer. ||a. Above 2. 58 and below -2. 58 | | ||b. Above 1. 00 and below -1. 00 | | ||c. Above 1. 96 and below -1. 96 | | ||d. Above 1. 65 and below -1. 65 | | If population standard deviation is known, we use Z test.

Two-tailed test with a=0. 01 =; areas under the normal curve = (1-0. 01)/2 = 0. 495 =; z critical value = 2. 58. The rejection area is for calculated z ; 2. 58 or z ; -2. 58 Correct Marks for this submission: 1/1. Question 13 Marks: 1 For a hypothesis test with an alternative hypothesis: µ ; 6,700, where is the rejection region for the hypothesis test located? Choose one answer. ||a. Upper or right tail | | ||b. Center | | ||c. Lower or left tail | | ||d. Both tails | | The null hypothesis is µ

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Qmet 252 Essay
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A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed, a sample of nine boxes of cake mix gave these shelf lives (in days): 215, 217, 218, 219, 216, 217, 217, 218 and 218. At the 0. 025 level, has the shelf life of the cake mix increased? Choose one answer. |[pic]|a. No, because computed t lies in the region of acceptance. [pic] | | |[pic]|b. Yes, because computed t
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