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QNT 275 Week 4 Apply: Connect Week 4 Case

At the end of 1990, 1991, and 1992, the average prices of a share of stock in a portfolio were $34.83, $34.65, and $31.26 respectively. To investigate the average share price at the end of 1993, a random sample of 30 stocks was drawn and their closing prices on the last trading day of 1993 were observed with a mean of 33.583 and a standard deviation of 19.149. Estimate the average price of a share of stock in the portfolio at the end of 1993 with a 90 percent confidence interval.

[27.646, 39.523]

[26.732, 40.434]

[32.514, 34.651]

[32.533, 34.633]

[32.269, 34.897]

The coffee and soup machine at the local subway station is supposed to fill cups with 6 ounces of soup. Ten cups of soup are bought with results of a mean of 5.93 ounces and a standard deviation of 0.13 ounces. How large a sample of soups would we need to be 95 percent confident that the sample mean is within 0.03 ounces of the population mean?

❏ 97

❏ 96

❏ 73

❏ 62

❏ 10

A researcher for a paint company is measuring the level of a certain chemical contained in a particular type of paint. If the paint contains too much of this chemical, the quality of the paint will be compromised. On average, each can of paint contains 10 percent of the chemical. How many cans of paint should the sample contain if the researcher wants to be 98 percent certain of being within 1 percent of the true proportion of this chemical?

❏ 4870

❏ 1107

❏ 26

❏ 645

3.

Award: 1 out of 1.00 point

When testing a hypothesis about a single mean, if the sample size is 51 and the population standard deviation is known, the correct test statistic to use is ___________.

r

z

t

p-value

5.

Award: 1 out of 1.00 point

The width of a confidence interval will be

narrower for 99 percent confidence than for 95 percent confidence.

wider for a sample size of 100 than for a sample size of 50.

narrower for 90 percent confidence than for 95 percent confidence.

wider when the sample standard deviation (s) is small than when s is large.

6.

Award: 1 out of 1.00 point

Using either the critical value rule or the p-value rule, if a one-sided null hypothesis for a single mean cannot be rejected at a given significance level, then the corresponding two-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will ______________ be rejected at the same significance level.

always

sometimes

never

7.

Award: 1 out of 1.00 point

If the sampled population has a mean of 48 and standard deviation of 16, then the mean and the standard deviation for the sampling distribution of x¯

for n = 16 are

4 and 1.

12 and 4.

48 and 4.

48 and 1.

48 and 16.

8.

Award: 1 out of 1.00 point

A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = 0.5. Suppose a random sample of 100 male students is selected and the GPA for each student is calculated. What is the probability that the random sample of 100 male students has a mean GPA greater than 3.42?

.0548

.4364

.9452

.5636

9.

Award: 1 out of 1.00 point

In the upcoming election for governor, the most recent poll, based on 900 respondents, predicts that the incumbent will be reelected with 55 percent of the votes. What is x¯σ

?

.00825

.0166

.0247

.0003

10.

Award: 1 out of 1.00 point

A research study investigated differences between male and female students. Based on the study results, we can assume the population mean and standard deviation for the GPA of male students are µ = 3.5 and σ = 0.5. Suppose a random sample of 100 male students is selected and the GPA for each student is calculated. Find the interval that contains 95.44 percent of the sample means for male students.

[3.45, 3.55]

[2.50, 4.50]

[3.35, 3.65]

[3.40, 3.60]

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. Find P( x¯

< 51.5).

.9641

.0359

.1389

.9999

For a fixed sample size, the lower we set α, the higher is the ___________.

Type I error

Type II error

random error

p-value

If the sampled population is finite and at least _____ times larger than the sample size, we treat the population as infinite.

5

20

30

10

A null hypothesis is not rejected at a given level of significance. As the assumed value of the mean gets further away from the true population mean, the Type II error will _____________.

increase

decrease

stay the same

randomly fluctuate

The number of defectives in 10 different samples of 100 observations each is the following: 1, 2, 1, 0, 2, 3, 1, 4, 2, 1. What is the estimate of the population proportion of defectives?

.017

.17

.016

.16

A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 lb and 24 lb, respectively, then based on a sample size of 36 boxes, what is the probability that the average weight of the boxes will exceed 94 lb?

34.13%

84.13%

15.87%

56.36%

16.87%

Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year. 225 flight records are randomly selected and the number of unoccupied seats is noted, with a sample mean of 11.6 seats and a standard deviation of 4.1 seats. How many flights should we select if we wish to estimate μ to within 5 seats and be 95 percent confident?

44

3

2

110

6

The t distribution approaches the _______________ distribution as the sample size ___________.

binomial, increases

binomial, decreases

z, decreases

z, increases

Using the critical value rule, if a two-sided null hypothesis is rejected for a single mean at a given significance level, the corresponding one-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will ______________ be rejected at the same significance level.

always

sometimes

never

The spread of the sampling distribution of x¯

is ____________ the spread of the corresponding population distribution sampling distribution.

larger than

smaller than

the same as

exactly ½

For the following hypothesis test, where H0: μ ≤ 10; vs. HA: μ> 10, we reject H0 at level of significance α and conclude that the true mean is greater than 10, when the true mean is really 8. Based on this information, we can state that we have

made a Type I error.

made a Type II error.

made a correct decision.

increased the power of the test.

When establishing the confidence interval for the average weight of a cereal box, assume that the population standard deviation is known to be 2 ounces. Based on a sample, the average weight of a sample of 20 boxes is 16 ounces. The appropriate test statistic to use is ________.

t

z

χ

p

A sample of 100 items has a population standard deviation of 5.1 and a mean of 21.6. Construct a 95 percent confidence interval for μ.

[11.60, 31.60]

[21.16, 22.04]

[20.60, 22.60]

[20.76, 22.43]

Recently, a case of food poisoning was traced to a particular restaurant chain. The source was identified and corrective actions were taken to make sure that the food poisoning would not reoccur. Despite the response from the restaurant chain, many consumers refused to visit the restaurant for some time after the event. A survey was conducted three months after the food poisoning occurred, with a sample of 319 former customers contacted. Of the 319 contacted, 29 indicated that they would not go back to the restaurant because of the potential for food poisoning. Construct a 95 percent confidence interval for the true proportion of the market who still refuse to visit any of the restaurants in the chain three months after the event.

[.059, .122]

[.090, .091]

[.000, .196]

[.240, .339]

[.118, .244]

4.

Award: 1 out of 1.00 point

The spread of the sampling distribution of ˉx is ____________ the spread of the corresponding population distribution sampling distribution.

larger than

smaller than

the same as

exactly ½

Assuming that the null hypothesis is true, the ______________ is the probability of observing a value of the test statistic that is at least as extreme as the value actually computed from the sample data.

α

β

p-value

Type I error

As the Type II error, β,of a statistical test increases, the power of the test _____________.

❏ increases

❏ decreases

❏ stays the same

❏ randomly fluctuates

————————————————————————————————————————

You manage Human Relations for your company. One of your sales managers has retired, leaving an opening. You are considering two different employees for the position. Both are highly qualified so you have decided to evaluate their sales performance for the past year.

Use the Week 4 Data Set to create and calculate the following in Excel®:

1. Determine the range of values in which you would expect to find the average weekly sales for the entire sales force in your company 90% of the time.

   • Calculate the impact of increasing the confidence level to 95%.
   • Calculate the impact of increasing the sample size to 150, assuming the same mean and standard deviation, but allowing the confidence level to remain at 90%.

2. Based on the calculated confidence interval for weekly sales on the sample of 50 reps at a 90% confidence level:

   • Calculate both Reps’ average weekly performance and highlight if it is greater than the population mean.

3. You want to determine whether the average weekly sales between Sales Rep A and Sales Rep B are statistically different in order to decide whom to promote.

   • Create Null and Alternative Hypothesis statements that would allow you to determine whether their sales performance is statistically different or not.
   • Use a significance level of .05 to conduct a t-test of independent samples to compare the average weekly sales of the two candidates.
   • Calculate the p-value.

4. Considering that individual you did not promote:

   • Determine whether this person’s average weekly sales are greater than the average weekly sales for the 50 sales reps whose data you used to develop confidence intervals.
   • Create Null and Alternative Hypothesis statements that would allow you to determine whether this person’s weekly average sales are greater than the sample of Sales Reps.
   • Use a significance level of .05 to conduct a t-test of independent samples to compare the average weekly sales of both.
   • Calculate the p-value.

Click the Assignment Files tab to submit.