Explain why we want rational samples in control charting.

In a survey of​ employees, a company reported that 52​% had confidence in the actions of senior management. To be 95​% confident that at least half of all employees have confidence in senior​ management, how many would have to be in the survey​ sample?

Please show and explain work

A study done by researchers at a university concluded that 90​% of all student athletes in a country have been subjected to some form of hazing. The study is based on responses from 1700 athletes. What is the margin of error and the​ 95% confidence interval for the​ study?

A certain species of snake is known to have a mean length of 18.2 inches with a standard deviation of 4.7 inches. Consider repeatedly choosing samples of 50 snakes of this species and finding the mean length of each sample.

a)What is the mean of this sampling distribution of x?

b)What is the standard deviation of this sampling distribution of x?

c)What is the shape of this sampling distribution? Explain how you know this.

d)Find the probability that the mean length for a sample of 50 snakes of this species is more than 20 inches

Show all work on paper.

Assume the random variable X is normally distributed with mean =50 and standard deviation =7. Find the 77 th percentile.

The mean incubation time of fertilized eggs is 2020 days. Suppose the incubation times are approximately normally distributed with a standard deviation of 11 day.

​(a) Determine the 15th percentile for incubation times.

​(b) Determine the incubation times that make up the middle 95​%.

**A company developed two commercials, A and B, to advertise for their product. Two random test groups were put together each with 100 individuals and each group watched one commercial and states if they would buy the product. Group A had 25 of the individuals say they would buy the product and Group B had 20 individuals say they would buy the product. It was concluded that commercial A was more effective.**

```{r}

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##b
**A randomized experiment was conducted to see if hormonal therapy was helpful for postmenopausal women in reducing cancer risk. One group was given a placebo and a second group administered the treatment. The treatment group showed that 107 of 8506 individuals developed cancer while the placebo group had 88 of 8102 individuals developed cancer. Does this data indicate that the therapy was effective. Use 1% level of significance**

```{r}

```

##c
**The following data comes from the FL Student Survey data. The two vectors represent the number of times in the past month that an individual read a newspaper, grouped by gender.**

**Test the hypothesis that females on average have read the newspaper more than males. Be sure to state your conclusion. Compare the conclusion drawn through hypothesis testing to the conclusion you would draw from a confidence interval. Use 5% level of significance.**
```{r}
females<-c(5,3,6,3,7,1,1,3,0,4,7,2,2,7,3,0,5,0,4,4,5,14,3,1,2,1,7,2,5,3,7)
males<-c(0,3,7,4,3,2,1,12,1,6,2,2,7,7,5,3,14,3,7,6,5,5,2,3,5,5,2,3,3)

Please Solve using R studio codes wih explanation

Suppose the life of a 1000gb solid state drive has a normal distribution with a mean of 42,000 hours and a standard deviation of 2400 hours. Suppose we have a random sample of n = 4 solid state drives, and xbar is the sample mean life of the 4 drives. What is P(41850 < xbar < 42300)

A population is believed to have a standard deviation of 16.7. A sample of size 68 is taken and the sample mean is calculated as 550.3. What is the margin of error (E) for a 90% confidence interval for the mean? Enter your answer to 2 decimal places.

A sample of size 6 is taken from a population with an unknown variance. The sample mean is 603.3 and the sample standard deviation is 189.8. Calculate a 95% confidence interval. What is the upper limit of the interval? Enter your answer to 1 decimal places.

A sample of size 67 is taken from a population with an unknown variance. The sample mean is 91.8 and the sample standard deviation is 6.7. Calculate a 95% confidence interval. What is the upper limit of the interval? Enter your answer to 1 decimal places.

A t-test on the mean of a population is performed with a sample of size 26 to generate a 90% confidence interval, what is the t value that should be used? Enter your answer to 3 decimal places.

The body temperatures in degrees Fahrenheit of a sample of adults in one small town are:

99.2

98.8

96.4

99.9

96.3

97.4

99.3

98.4

98.1

97.9

98.7

98.5

96.6

Assume body temperatures of adults are normally distributed. Based on this data, find the 95% confidence interval of the mean body temperature of adults in the town. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places. Assume the data is from a normally distributed population.

95% C.I. = ________

Consider the following statements. (i) If a hypothesis is tested at the 5% significance level with a given data set, then there is a higher chance that the null hypothesis will be rejected than if that same hypothesis is tested at the 1% significance level with the same data set. (ii) If a hypothesis test is performed at the 5% significance level, and if the null hypothesis is actually true, then there is a 5% chance that the null hypothesis will be rejected. (iii) P(Type I Error) + P(Type II Error) = 1. Determine which of the above statements are true (1) or false (2).

The number of miles a motorcycle, X, will travel on one gallon of gasoline is modeled by a normal distribution with mean 44 and standard deviation 5. If Mike starts a journey with one gallon of gasoline in the motorcycle, find the probability that, without refueling, he can travel more than 50 miles.

Sherds of clay vessels were put together to reconstruct rim diameters of the original ceramic vessels at the Wind Mountain archaeological site†. A random sample of ceramic vessels gave the following rim diameters (in centimeters).

15.9

13.4

22.1

12.7

13.1

19.6

11.7

13.5

17.7

18.1

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean x and sample standard deviation s. (Round your answers to one decimal place.)

x =	cm
s =	cm

(b) Compute a 99% confidence interval for the population mean μ of rim diameters for such ceramic vessels found at the Wind Mountain archaeological site. (Round your answers to one decimal place.)

lower limit	cm
upper limit	cm

1. x bar and R control Charts

A quality control inspector at the Company B has taken twenty-five samples with four observations each of the sample weight (g). The data are shown in the table. Construct x bar and R control charts for these data. Identify any out-of- control points. Assume these points (if any) are assignable. Remove them and recalculate the control limits. Construct the revised x bar and R control charts. Submit data (spreadsheet) and charts.

Comment on the validity of the revised chart?

Sample	Weight in g
	X1	X2	X3	X4
1	32	36	33	35
2	36	31	35	34
3	30	32	31	33
4	29	34	38	32
5	32	37	36	33
6	35	38	43	37
7	30	37	35	33
8	29	33	28	31
9	31	33	33	32
10	35	29	35	31
11	36	40	32	31
12	33	30	29	35
13	33	30	34	34
14	35	37	36	41
15	33	35	37	30
16	31	33	34	36
17	29	34	30	37
18	34	32	34	30
19	36	35	33	31
20	33	31	33	31
21	29	32	37	33
22	30	30	29	31
23	33	32	35	30
24	36	34	31	33
25	34	35	30	30

Do a two-sample test for equality of means assuming unequal variances. Calculate the p-value using Excel.

(a-1) Comparison of GPA for randomly chosen college juniors and seniors:

x⎯⎯1x¯1 = 4.75, s<sub>1</sub> = .20, n<sub>1</sub> = 15, x⎯⎯2x¯2 = 5.18, s<sub>2</sub> = .30, n<sub>2</sub> = 15, α = .025, left-tailed test.
(Negative values should be indicated by a minus sign. Round down your d.f. answer to the nearest whole number and other answers to 4 decimal places. Do not use "quick" rules for degrees of freedom.)

d.f.

t-calculated

p-value

t-critical

b-1) Comparison of average commute miles for randomly chosen students at two community colleges:

x⎯⎯1x¯1 = 25, s<sub>1</sub> = 5, n<sub>1</sub> = 22, x⎯⎯2x¯2 = 33, s<sub>2</sub> = 7, n<sub>2</sub> = 19, α = .05, two-tailed test.
(Negative values should be indicated by a minus sign. Round down your d.f. answer to the nearest whole number and other answers to 4 decimal places. Do not use "quick" rules for degrees of freedom.)

d.f.

t-calculated

p-value

t-critical

(c-1) Comparison of credits at time of graduation for randomly chosen accounting and economics students:

x⎯⎯1x¯1 = 150, s<sub>1</sub> = 2.8, n<sub>1</sub> = 12, x⎯⎯2x¯2 = 143, s<sub>2</sub> = 2.7, n<sub>2</sub> = 17, α = .05, right-tailed test.
(Negative values should be indicated by a minus sign. Round down your d.f. answer to the nearest whole number and other answers to 4 decimal places. Do not use "quick" rules for degrees of freedom.)

d.f.

t-calculated

p-value

t-critical

1)- A set of solar batteries is used in a research satellite. The satellite can run on only one battery, but it runs best if more than one battery is used. The variance σ<sup>2</sup> of lifetimes of these batteries affects the useful lifetime of the satellite before it goes dead. If the variance is too small, all the batteries will tend to die at once. Why? If the variance is too large, the batteries are simply not dependable. Why? Engineers have determined that a variance of σ<sup>2</sup> = 23 months (squared) is most desirable for these batteries. A random sample of 29 batteries gave a sample variance of 15.6 months (squared). Using a 0.05 level of significance, test the claim that σ<sup>2</sup> = 23 against the claim that σ<sup>2</sup> is different from 23.

(a) What is the level of significance?


State the null and alternate hypotheses.

H<sub>o</sub>: σ<sup>2</sup> = 23; H<sub>1</sub>: σ<sup>2</sup> < 23H<sub>o</sub>: σ<sup>2</sup> = 23; H<sub>1</sub>: σ<sup>2</sup> > 23    H<sub>o</sub>: σ<sup>2</sup> > 23; H<sub>1</sub>: σ<sup>2</sup> = 23H<sub>o</sub>: σ<sup>2</sup> = 23; H<sub>1</sub>: σ<sup>2</sup> ≠ 23

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)


What are the degrees of freedom?


What assumptions are you making about the original distribution?

We assume a normal population distribution.We assume a exponential population distribution.    We assume a uniform population distribution.We assume a binomial population distribution.

(c) Find or estimate the P-value of the sample test statistic.

P-value > 0.1000.050 < P-value < 0.100    0.025 < P-value < 0.0500.010 < P-value < 0.0250.005 < P-value < 0.010P-value < 0.005

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

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 5% level of significance, there is insufficient evidence to conclude that the variance of battery life is different from 23.At the 5% level of significance, there is sufficient evidence to conclude that the variance of battery life is different from 23.    

(f) Find a 90% confidence interval for the population variance. (Round your answers to two decimal places.)

lower limit
upper limit

(g) Find a 90% confidence interval for the population standard deviation. (Round your answers to two decimal places.)

lower limit	months
upper limit	months

2)- Anystate Auto Insurance Company took a random sample of 376 insurance claims paid out during a 1-year period. The average claim paid was $1550. Assume σ = $252.

Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

lower limit	$
upper limit	$

Find a 0.99 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

lower limit	$
upper limit	$