BUAL 2650 Test 1
In a manufacturing process, a random sample of 9 manufactured bolts has a mean length of 3inches with a variance of .09 and is normally distributed. What is the 90 percent confidence intervalfor the true mean length of the manufactured bolt?
2.8140 to 3.1860
In a manufacturing process, a random sample of 36 manufactured bolts has a mean length of 3inches with a standard deviation of .3 inches. What is the 99 percent confidence interval for the truemean length of the manufactured bolt?
2.864 to 3.136
In a manufacturing process, we are interested in measuring the average length of a certain type ofbolt. Past data indicate that the standard deviation is .25 inches. How many manufactured boltsshould be sampled in order to make us 95 percent confident that the sample mean bolt length iswithin .02 inches of the true mean bolt length?
601
Which of the following statements is not a property of the normal probability distribution?
95.44 percent of all possible observed values of the random variable x are within plus or minus three standard deviations of the population mean
If the random variable x is normally distributed, ______ percent of all possible observed valuesof x will be within three standard deviations of the mean
99.73
exponential curve
J curve
__________ values of the standard deviation result in a normal curve that is wider and flatter.
Larger
Rejecting a true null hypothesis is called a ______ error.
Type I
________ says that if the sample size is sufficiently large, then the sample means are approximately normally distributed.
The Central Limit Theorem
discrete variable
a quantitative variable that has either a finite number of possible values or a countable number of possible values
uniform curve
constant probability
As the standard deviation (σ) decreases, the width of the confidence interval ________
decreases
qualitative data
descriptive data
The area under the curve of a valid continuous probability distribution must
equal 1
For nonnormal populations, as the sample size (n) ________, the distribution of sample means approaches a(n) ________ distribution.
increases, normal
The specific shape of each normal distribution is determined by its ____________ and ______________.
mean, standard deviation
is probability under a curve ever = 0 ?
no
The normal approximation of the binomial distribution is appropriate when
np >= 5 and n(1-p)>=5
The exact spread of the t distribution depends on the ________.
number of degrees of freedom
quantitative data
numerical data
A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes. The opinion poll recently sampled 1,500 voting agecitizens. 1,020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66. Identify the null hypothesis.
p <= 0.66
It is appropriate to use the uniform distribution to describe a continuous random variable x when
relative frequencies of all possible values of x are about the same
A confidence interval for the population mean is an interval constructed around the _______
sample mean
The z value tells us the number of _____ that a value of x is from the mean
standard deviations
In testing H0: μ = 23; versus HA: μ > 23 using the critical value rule, when x ̄x ̄ = 26, s = 6,and n = 20, what is the value of the test statistic? Assume that the population from which thesample is selected is normally distributed.
t = 2.24
continuous probability distribution
the curve f(x) is the continuous probability distribution of the continuous random variable x if the probability that x will be in a specified interval of numbers is the area under the curve f(x) corresponding to the interval
The fill weight of a certain brand of adult cereal is normally distributed with a mean of 910 grams and a standard deviation of 5 grams. We calculated the value of z for a specific box of this brand of cereal, and the z value was negative. This negative z value indicates that
the fill weight is less than 910 grams
normal curve
the symmetrical bell-shaped curve that describes the distribution of many physical and psychological attributes. Most scores fall near the average, and fewer and fewer scores lie near the extremes.
When the population is normally distributed, population standard deviation σ is unknown, and thesample size is n = 15, the confidence interval for the population mean μ is based on
the t distribution
A continuous probability distribution having a rectangular shape, where the probability is evenly distributed over an interval of numbers is a(n) __________ distribution
uniform
When testing a hypothesis about a single mean, if the sample size is 51 and the population standarddeviation is known, the correct test statistic to use is ________
z
The mean of a standard normal distribution is always equal to
0
Packages of sugar bags for Sweeter Sugar Inc. have an average weight of 16 ounces and astandard deviation of .2 ounces. The weights of the sugar packages are normally distributed. What isthe probability that 16 randomly selected packages will have a weight in excess of 16.075 ounces?
0.0668 P[z > (16.075 − 16)/(.2/√16)] = P(z > 1.5) = 1.00 − .9332 = .0668
Find P(x ̄ < 35) if μ = 40, σx = 16, n = 16
0.1056
Given that the length an athlete throws a hammer is a normal random variable with mean 50 feetand standard deviation 5 feet, what is the probability he throws it no less than 55 feet?
0.1587 Z = (55 − 50)/5 = 1P(X ≥ 55) = 1 − .8412 = .1587
What is the probability that a standard normal random variable will be between 0.3 and 3.2?
0.3814
Find P(x ̄> 172), if μ = 175 and σ2 (variance) = 9
0.8413 z=(172 − 175)/9-√=−1P(x>172)=1.00 − .1587