Qmet 252

Topics: Statistical hypothesis testing, Statistics, Null hypothesis Pages: 7 (1381 words) Published: August 31, 2010
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 is less than the critical value. [pic] | | |[pic]|c. Yes, because computed t is greater than the critical value. [pic] | | |[pic]|d. No, because 217.24 is quite close to 216. [pic] | |

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.

Marks for this submission: 2/2.
Question 2
Marks: 1
If α = 0.05 for a two-tailed test, how large is the acceptance area? Choose one answer.
|[pic]|a. 0.025 [pic] | |
|[pic]|b. 0.975 [pic] | |
|[pic]|c. 0.05 [pic] | |
|[pic]|d. 0.95 [pic] | |

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.

|[pic]|a. To the left of -1.345 or to the right of 1.345 [pic] | | |[pic]|b. To the left of -1.645 or to the right of 1.645 [pic] | | |[pic]|c. To the left of -1.282 or to the right of 1.282 [pic] | | |[pic]|d. Between -1.761 and 1.761 [pic] | |

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.

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.

|[pic]|a. Cut back production [pic] | | |[pic]|b. Cannot determine based on information given [pic] | | |[pic]|c. None of these [pic] | | |[pic]|d. Do not cut back production [pic] | |

It is a testing concerning proportions.

Ho: π >= 0.4
H1: π < 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 –...
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