A sample of 35 cars of a certain kind had an average mileage of 36.2 mpg. Assuming that mileage is approximately normally distributed with standard deviation 4 mpg, test the hypothesis that the average mileage for all cars of this type is no less than 34.2 mpg at the 0.01 significance level. Give the value of p you find to two decimal places, and choose the correct conclusion:

p=

Problems 1-4 assume a normally distributed population with a mean = 48 and standard deviation = 5. Be sure to sketch the curve, include formulas & work, round appropriately, and circle your final answer.

1. What percent of the scores fall:

at or below 54?

at or above 40?

2. (6 points) What proportion of scores lie between:

31 and 48?

31 and 54?

3. (4 points) Suppose we took a sample of 5000 scores from this distribution.

Of those 5000 scores, how many would you expect to lie between31 and 48?

Of those 5000 scores how many would you expect to lie between 31 and 54?

4. If you select one person at random from this population and find his/her score on this variable to be 63 would you be surprised (yes/no)? Why/why not?

5. (4 points) Later in the semester we will focus on z-scores that capture the middle 95% of the distribution.
   1. Find the two z-scores that capture the middle 95% of the distribution. Be sure to show your work. (Hint: remember that the normal curve is symmetrical.)

What two z-scores would we use if we want to capture the middle 99% of the distribution?

(I) You may consider using function prop.test to perform the above hypothesis test.

(II) Present complete procedures of hypothesis testing for the above problem such as null hypothesis, alternative hypothesis, significance level, test statistics value, p-value etc..in your findings.

(III) State your conclusion clearly.

A cell-phone store sold 150 smartphones of Brand A and 14 of them returned as defective items. Besides that, the cell-phone store sold also 125 smartphones of Brand B and 15 phones of them retuned as defective items. Is there any statistical evidence that Brand A has a smaller chance of being returned than Brand B at:

(i) 1% significance level?

(ii) 5% significance level?

(iii) 10% significance level?

Justify your findings.

The overhead reach distances of adult females are normally distributed with a mean of

202.5 cm202.5 cm

and a standard deviation of

8.6 cm8.6 cm.

a. Find the probability that an individual distance is greater than

215.90215.90

cm.

b. Find the probability that the mean for

2020

randomly selected distances is greater than 200.70 cm.200.70 cm.

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

The types of raw materials used to construct stone tools found at an archaeological site are shown below. A random sample of 1486 stone tools were obtained from a current excavation site.

Use a 1% level of significance to test the claim that the regional distribution of raw materials fits the distribution at the current excavation site.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: The distributions are different.
H₁: The distributions are different.

H₀: The distributions are different.
H₁: The distributions are the same.     

H₀: The distributions are the same.
H₁: The distributions are different.

H₀: The distributions are the same.
H₁: The distributions are the same.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)


Are all the expected frequencies greater than 5?

Yes or No     

What sampling distribution will you use?

chi-square

normal     

uniform

Student's t

binomial

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)


(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since the P-value > α, we fail to reject the null hypothesis.

Since the P-value > α, we reject the null hypothesis.     

Since the P-value ≤ α, we reject the null hypothesis.

Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 0.01 level of significance, there is sufficient evidence to conclude that the regional distribution of raw materials and the current excavation site distribution are not independent.

At the 0.01 level of significance, there is insufficient evidence to conclude that the regional distribution of raw materials and the current excavation site distribution are not independent.     

Gas Mileage. Based on tests of the Chevrolet Cobalt, engineers have found that the miles per gallon in highway driving are normally distributed, with a mean of 32 MPG and a standard deviation of 3.5 MPG.

a) What is the probability that a randomly selected Cobalt gets more than 34 MPG?

b) Suppose that 10 Cobalts are randomly selected and the MPG for each car are recorded. What is the probability that the mean MPG exceeds 34 MPG?

c) Suppose 20 Cobalts are randomly selected and the MPG for each car are recorded. What is the probability that the mean MPG exceeds 34 MPG?

QUESTION 1

1. A random group of oranges were selected from an orchard to analyze their ripeness. The data is shown

   below:

   Ready to pick

   Ripe

   Ready in three days

   Ready in one week

   Ready in two weeks

   Number of oranges

   11

   20

   13

   17

   Based on the time of year, the orchard owner believes that 30% of the oranges are ready for picking now,

   30% will be ready in three days, 30% will be ready in one week, and 10% will be ready in two weeks.
   Is there evidence to reject this hypothesis at a  .05 significance level?  

   		There is evidence to reject the claim that the oranges are distributed as claimed because the test value 24.082 > 9.488
   		There is not evidence to reject the claim that the oranges are distributed as claimed because the test value 5.991 < 24.082
   		There is evidence to reject the claim that the oranges are distributed as claimed because the test value 24.082 > 7.815
   		There is not evidence to reject the claim that the oranges are distributed as claimed because the test value 9.488 < 24.082

Calculate raw scores from the following z-scores. The mean of the original dataset was 10, and the standard deviation was 3.

1. What is the raw score for a z-score of -2.89?

2. What is the raw score for a z-score of +0.74?

3. What is the raw score for a z-score of +1.18?

4. What is the raw score for a z-score of -0.94?

5. What is the raw score for a z-score of -1.26?

12.52 Christmas Drink.(P576)

In a 2014 nationwide Harris Poll survey about beverage preferences, 195 1 American adults were asked about their preferred beverages during different holidays throughout the year. Overall, 47% of the adults voted for table wine as their preferred beverage for Christmas. Determine and interpret a 95% confidence interval for the proportion, p, of all American adults who prefer wine during holiday

Empirical studies have provided support for
the belief that an ordinary share’s annual
rate of return is approximately normally
distributed. Suppose that you have invested in
the shares of a company for which the annual
return has an expected value of 16% and a
standard deviation of 10%.
a Find the probability that your one-year
return will exceed 30%.
b Find the probability that your one-year
return will be negative.
c Suppose that this company embarks on
a new, high-risk, but potentially highly
profi table venture. As a result, the return
on the share now has an expected value
of 25% and a standard deviation of 20%.
Answer parts (a) and (b) in light of the
revised estimates regarding the share’s
return.
d As an investor, would you approve of the
company’s decision to embark on the new
venture?

Describe when ANOVA is used and why it is necessary.

The college Physical Education Department offered an Advanced First Aid course last summer. The scores on the comprehensive final exam were normally distributed, and the zscores for some of the students are shown below.

(d) If the mean score was μ = 146 with standard deviation σ = 23, what was the final exam score for each student? (Round your answers to the nearest whole number.)

The data below represents a sample of 22 people and how they voted on a referendum in a recent election. You are a social scientist who is interested in investigating age differences in voting patterns.

1. State the kind of statistical test you will perform (i.e., chi-square or an ANOVA).

HINT: Look at the types of variables available to you, which test is best suited for these types of variables with this many categories?

2. State the research and null hypotheses using words and symbols when applicable.

3. Report the degrees of freedom and the corresponding critical value for your test.

4. Compute the test statistic (i.e., chi-square or an ANOVA).

HINT: Make a computation table to keep track of your work.

5. Using your critical and obtained values, make a decision regarding your null hypothesis.

6. What conclusions can you draw about the voting behaviors of older and younger folks? Even if you don’t have enough information to compute the measure of association, which one would be appropriate for this test? What do you think it would indicate in terms of strength and direction of the observed relationship?

HINT: Make sure you respond to all of these questions using sentences that make sense!

Search on the following three phrases:

• Insertion Anomaly
• Update Anomaly
• Deletion Anomaly

Determine whether the BEST, most common interpretation of the given statement is:

     TRUE - Select 1

     FALSE - Select 2

Question 1 options

When the population standard deviation sigma is assumed known, a confidence interval can assume NORMALITY of the SAMPLE MEAN if the sample size is greater than 30.

INCREASING the confidence level of a confidence interval from 90% to 99% makes the interval SHORTER.

A CONFIDENCE INTERVAL can be interpreted as the single best ESTIMATE of a population parameter.

As the sample size INCREASES for computing a confidence interval, the width of the confidence interval DECREASES.

For a PROBABILITY DENSITY FUNCTION, the area between two values aand b is the probability a randomly selected individual will have a value between a and b.

A Z-SCORE can be interpreted for a value as the value's number of standard deviation above or below the mean.

A NORMAL distribution will have an approximately SYMMETRIC histogram.

As the STANDARD DEVIATION decreases for a normal distribution, the values become LESS concentrated around the MEAN.

The goal when using confidence intervals is to have WIDE INTERVALS to be assured that the interval contains the population parameter.

A SYMMETRIC histogram implies the plotted variable is NORMALLY distributed.