Question

1) Golf-course designers have become concerned that old courses are becoming obsolete since new technology has given golfers the ability to hit the ball so far. Designers, therefore, have proposed that new golf courses need to be built expecting that the average golfer can hit the ball more than 255255 yards on average. Suppose a random sample of 135 golfers be chosen so that their mean driving distance is 252.5 yards. The population standard deviation is 42.6 Use a 5% significance level.

Calculate the followings for a hypothesis test where ?0:?=255: and ?1:?<255

(a)    The test statistic is    

(b)    The P-Value is

The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) ? and standard deviation ?=0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5 mg. Now, suppose a reporter wants to test whether the mean nicotine content is actually higher than advertised. He takes measurements from a SRS of 20 cigarettes of this brand. The sample yields an average of 1.45 mg of nicotine. Conduct a test using a significance level of ?=0.05

(a) The test statistic  

(b) The critical value, z* =

A random sample of 100 observations from a population with standard deviation 11.99 yielded a sample mean of 92.

1. Given that the null hypothesis is ?=90 and the alternative hypothesis is ?>90 using ?=.05α, find the following:

(a) Test statistic =
(b)  P - value:

Given that the null hypothesis is ?=90 and the alternative hypothesis is ?≠90 using ?=.05α, find the following:
(a) Test statistic ==  
(b)  P - value:

It is necessary for an automobile producer to estimate the number of miles per gallon achieved by its cars. Suppose that the sample mean for a random sample of 150 cars is 30.7 miles and assume the standard deviation is 2.1 miles. Now suppose the car producer wants to test the hypothesis that ? the mean number of miles per gallon, is 28 against the alternative hypothesis that it is not 28. Conduct a test using ?=.05 by giving the following:

(a)    positive critical ? score    

(b)    negative critical ? score    

(c)    test statistic

35 people are randomly selected and the accuracy of their wristwatches is checked, with positive errors representing watches that are ahead of the correct time and negative errors representing watches that are behind the correct time. The 35 values have a mean of 107sec and a standard deviation of 218sec. Use a 0.01significance level to test the claim that the population of all watches has a mean of 0 sec.

The test statistic is

The P-Value is

Given the significance level ?=0.07 find the following:

(a)    left-tailed ?z value
?=

(b)    right-tailed z value
?=

(c)    two-tailed ? value
|?|=

Answer 1

1.