Refer to the accompanying data display that results from a sample of airport data speeds in mbps.complete parts (a) through (c) below .
T INTERVAL (13.046,22.15)
_
x=17.598
sx=16.01712719
n=50

a.express the confidence interval in the format that uses the "less than" symbol. Given that the original listed data use one decimal place, round the confidence interval limits accordingly.
mbps <u <Mbps

A researcher interested in the working habits of students at RCC randomly selects 300 students and

finds that 23% have a full time job.

(a) Did the study use population or sample data? Explain.

(b) If sample data was used, what is the population it was drawn from?

(c) Is the figure 23% a parameter or a statistic? Explain.

(d) Is the variable qualitative or quantitative? Explain.

1. In the 2008 General Social Survey, incomes of married respondents were classified as above average, average, and below average. Respondents also answered a question about marital happiness as not happy, pretty happy, or very happy. The results are below:

Conduct an appropriate test to determine whether or not there is a statistically significant association between marital happiness and income at the 5% significance level.

1. Based on the significance level at which you are testing, what is (are) the critical value(s) for the test?
2. Calculate the appropriate test statistic, showing all your work. You should explicitly display (1) expected values for each cell and (2) the test statistic contribution of each cell in addition to calculating the overall test statistic.
3. Calculate the corresponding p-value from the appropriate table or online calculator.
4. What conclusions can you draw from the hypothesis test? Be sure to comment on evidence from both the test statistic and p-value.

Can hair length be used to predict the height of a person? To try to answer this, the following random subset of data were collected from our class’s data:

Hair length:       8        12        18        24        1        4          24        2                   

Height:            68       60        61        67        67        70        68        70

1. Is there a significant correlation between hair length and height? Use α=.05.
2. Calculate the coefficient of determination. What does this value say about the relationship between hair length and height?
3. What would you expect the height to be of a person with 4 inches of hair?
4. Create a 90% prediction interval for the height of a person with 4 inches of hair.

Suppose that a sample of 15 women had a mean heart rate of 73.93 and a sample standard deviation of 8.42. Assume that the distribution of women’s heart rates is normal. Use this data to answer the following:

a.) Construct the lower bound for a 99% confidence interval for the population mean heart rate of all women. Round answers to the hundredth.

b.) Construct the upper bound for a 99% confidence interval for the population mean heart rate of all women. Round answers to the hundredth.

c.) You just constructed a 99% confidence interval for the population mean heart rate of all women. If we left the confidence level the same, what would happen to the width of the interval if we increased the sample size to 100 women?

d.) You just constructed a 99% confidence interval for the population mean heart rate of all women. The American Medical Association claims the average heart rate for women is 69 bpm. Does your interval support or contradict this claim?

A random sample of 49 colleges yielded a mean cost of college education of $30,500 per year. Assume that the population standard deviation is $3000 and college costs are normally distributed.

a.) Calculate the standard error of the mean. Round to the hundredth.

b.) Calculate the lower bound for a 90% confidence interval for the population mean cost of education. Round to the hundredth.

c.) Calculate the upper bound for a 90% confidence interval for the population mean cost of education. Round to the hundredth

d.) You just constructed a 90% confidence interval for the population mean cost of education. How will the interval change if we increase the confidence to 99%?

e.) How large a sample is needed if we wish to estimate the population mean cost of college education within $200 with 90% confidence? Round answer up to the next whole number.

#14) A researcher collected data on the eating habits of 64 Americans in 2018 and finds that they eat an average of 125 lbs of cheese per year with a sample standard deviation of 40 lbs.

a) Can we definitively say that Americans eat more than 120 lbs of cheese per year? Show all steps of the hypothesis test to test this question. (15pts)

b) Find the 95% confidence interval for cheese an average American consumes per year. (5pts)

Protein content in a particular farmer’s soybean crop is normally distributed with a mean of 40 grams and a standard deviation of 20 grams. Suppose we take samples of size 100 soy plants. Use this data to answer the following:

a.) Find the probability that a randomly chosen soy plant’s protein content will be less than 38 grams. Write answer as decimal rounded to the thousandth.

b.) Find the probability the sample mean protein content will be less than 38 grams. Write answer as decimal rounded to the thousandth.

1-A manager of an e-commerce company would like to determine average delivery time of the products. A sample of 25 customers is taken. The average delivery time in the sample was four days. Suppose the delivery times are normally distributed with a standard deviation of 1.2 days.

a) Provide a 95 % confidence interval for the mean delivery time.

b) The manager claims that the average delivery time of their products does not exceed 3 days. Write the null and alternative hypothesis regarding to the claim of the manager.

c) Test the manager’s claim at 95 % confidence level.

d) Write the conclusion of your result 3)

2- For an effective parental skill study, a researcher asked: How many hours do your kids watch the television during a typical week in Barcelona? The mean of 100 Kids (ages 6-11) spend about 28 hours a week in front of the TV. Suppose the study follows a normal distribution with standard deviation 5.

a) Estimate the mean of all kids (ages 6-11) in Barcelona, using 99% confidence interval. (show all the calculations)

b) Write the conclusion of your result

The ability to find a job after graduation is very important to GSU students as it is to the students at most colleges and universities.

Suppose we take a poll (random sample) of 3613 students classified as Juniors and find that 2956 of them believe that they will find a job immediately after graduation.

What is the 99% confidence interval for the proportion of GSU Juniors who believe that they will, immediately, be employed after graduation.

The urinary fluoride concentration (parts per million) was measured both for a sample of livestock grazing in an area previously exposed to fluoride pollution and for a similar sample grazing in an unpolluted region:

Polluted. 21.3. 18.7 23.0. 17.1. 16.8. 20.9. 19.7

Unpolluted. 14.2. 18.3. 17.2. 18.4. 20.0

Does the data indicate strongly that true average fluoride concentration for livestock grazing in the polluted region is larger than for the unpolluted region? Use the appropriate test at level α = 0.01.

Confirmed Cases, X Hospitalizations, Y 2605 482 1833 334 1532 321 1474 283 1465 431 1062 154 643 113 626 115 456 54 384 71 373 108 362 87 329 61 302 44 292 66 288 116 282 89 282 50 263 36 252 64 212 73 206 52 201 14 199 9 195 33 188 32 183 39 181 39 170 10 167 28 167 30 165 29 163 38 161 48 159 35 156 21 155 32 144 23 142 28 137 25 135 39 133 36 128 28 126 9 114 32 112 36 110 33 109 33 100 27 98 17 85 6 81 25 76 17 76 13 73 25 72 21 70 15 67 10 64 8 62 8 59 0 58 11 57 7 56 9 54 15 53 11 53 16 53 11 51 11 51 14 50 8 49 2 49 10 48 16 48 10 46 5 46 10 44 14 43 13 39 10 39 7 39 14 39 6 35 10 34 7 34 11 34 4 33 6 32 11 32 13 31 6 31 8 29 6 29 1 29 6 28 7 27 6 26 4 25 5 24 2 24 3 24 3 24 5 23 4 23 4 22 3 22 4 22 7 21 1 21 8 21 4 21 11 20 7 20 4 20 2 20 3 20 7 19 1 19 2 17 4 17 3 17 4 17 4 16 2 16 3 16 7 16 8 15 1 15 2 14 2 14 3 14 2 14 6 13 3 12 3 11 2 10 3 10 5 10 4 9 0 9 2 9 0 9 5 8 2 8 2 8 2 8 4 7 2 7 1 7 2 5 0 4 0 4 2 4 2 3 2 3 0 2 1 2 0 0 0 0 0

Please use excel to complete this. can you send an excel file back

The average life of a certain type of motor is 10 years with a standard deviation of 2 years. You are interested in measuring the life time of this motor by conducting a survey asking customers’ experiences. Use this information and answer Question 4a to 4h.

Question 4a: What is the probability distribution of the life time of the motor, X?

Question 4b: In the first week, you were able to obtain 25 survey responses on the life of the motor you are studying. What is distribution of the average life of the motor, X ¯?

Question 4c: After a month-long survey, you collected 367 responses. What would be the expected value of the average life time of the motor using the survey responses?

Question 4d: After a month-long survey, you collect 367 responses. What is the probability that the average life time of the motor is greater than 10 years and 3 months? (Use four decimal places)

Question 4e: After a month-long survey, you collect 146 responses and find that the average life of the motor is 10.02 years. What is the upper limit of a two-sided 95% confidence interval of the true average life of the motor? (Use four decimal places)

A survey of 25 randomly selected customers found the ages shown​ (in years). The mean is 31.96 years and the standard deviation is 10.12 years.

​a) Construct a 95​% confidence interval for the mean age of all​ customers, assuming that the assumptions and conditions for the confidence interval have been met.

​b) How large is the margin of​ error?

​c) How would the confidence interval change if you had assumed that the standard deviation was known to be 11.0 ​years?

Birth weight and gestational age. The Child Health and Development Studies considered pregnancies among women in the San Francisco East Bay area. Researchers took a random sample of 50 pregnancies and used statistical software to construct a linear regression model to predict a baby's birth weight in ounces using the gestation age (the number of days the mother was pregnant). A portion of the computer output and the scatter plot is shown below. Round all calculated results to four decimal places.

1. Use the computer output to write the estimated regression equation for predicting birth weight from length of gestation.

Birth weight =  +  * gestation

2. Using the estimated regression equation, what is the predicted birth weight for a baby with a length of gestation of 283 days?

3. The recorded birth weight for a baby with a gestation of 283 days was 125 ounces. Complete the following sentence:

The residual for this baby is  . This means the birth weight for this baby is  ? higher than the same as lower than  the birth weight predicted by the regression model.

4. Complete the following sentence:

% of the variation in  ? Birth weight Gestation age Babies Pregnancy  can be explained by the linear relationship to  ? Birth weight Gestation age Babies Pregnancy .

Do the data provide evidence that gestational age is associated with birth weight? Conduct a t-test using the information given in the R output and the hypotheses

?0:?1=0H0:β1=0 vs. ??:?1≠0HA:β1≠0

3. Test statistic =

4. Degrees of freedom =

5. P-value =

6. Based on the results of this hypothesis test, there is  ? little evidence some evidence strong evidence very strong evidence extremely strong evidence  of a linear relationship between the explanatory and response variables.

7. Calculate a 90% confidence interval for the slope, ?1β1. (  ,  )