The graph illustrates the distribution of test scores taken by College Algebra students. The maximum possible score on the test was 110, while the mean score was 80 and the standard deviation was 7. 59 66 73 80 87 94 101 Distribution of Test Scores What is the approximate percentage students who scored between 73 and 87 on the test? Incorrect% What is the approximate percentage of students who scored lower than 59 on the test? Incorrect% What is the approximate percentage of students who scored less than 66 on the test? Incorrect% What is the approximate percentage of students who scored between 66 and 94 on the test? Incorrect%

Examine the three samples obtained independently from three populations:

Population Data 3

1. Conduct a one-way analysis of variance on the data assuming the populations have equal variances and the populations are normally distributed. Use alpha = 0.05.
2. If warranted, use the Tukey-Kramer procedure to determine which populations have different means. Use an alpha level of 0.05.

An industrial company claims that the mean pH level of the water in a nearby river is 6.8 you randomly select 19 water sample mean and standard deviation are 6.7 and 0.24, respectively. is there enough evidence to reject the company claim at a=0.05? Assume the population normally distributed.

In #29-32, use the following information. Use a 0.025 level of significance to test the claim that vehicle speeds at a certain location have a mean above 55 km/h . A random sample of 50 vehicles produces a mean of 61 3. km/h and standard deviation of 3 3. km/h .

29. Give the null hypothesis in symbolic form. (a) H0 :µ > 55 (b) H0 :µ ≥ 55 (c) H0 :µ ≤ 55 (d) H0 :µ < 55 (e) H0 :µ = 55

30. Determine the appropriate test statistic. (a) z = 12.1 (b) z = 13.5 (c) p = 10.2 (d) p = 4.28 (e) z = 8.31

31. Find the appropriate critical value(s). (a) z = −1.96 (b) z = 1.96 (c) z = −1.96, z = 1.96 (d) z = −2.24, z = 2.24 (e) t = −1.96

32. Make the appropriate decision. (a) Reject H0 (b) Fail to reject H

The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Let x₁ be a random variable that represents the time interval (in minutes) between Old Faithful eruptions for the years 1948 to 1952. Based on 9580 observations, the sample mean interval was x₁ = 61.8 minutes. Let x₂ be a random variable that represents the time interval in minutes between Old Faithful eruptions for the years 1983 to 1987. Based on 23,000 observations, the sample mean time interval was x₂ = 69.2 minutes. Historical data suggest that σ₁ = 8.49 minutes and σ₂ = 11.78 minutes. Let μ₁ be the population mean of x₁ and let μ₂ be the population mean of x₂.(a) Compute a 99% confidence interval for μ₁ – μ₂. (Use 2 decimal places.)

(b) Comment on the meaning of the confidence interval in the context of this problem. Does the interval consist of positive numbers only? negative numbers only? a mix of positive and negative numbers? Does it appear (at the 99% confidence level) that a change in the interval length between eruptions has occurred? Many geologic experts believe that the distribution of eruption times of Old Faithful changed after the major earthquake that occurred in 1959.

Because the interval contains only positive numbers, we can say that the interval length between eruptions has gotten shorter.Because the interval contains both positive and negative numbers, we can not say that the interval length between eruptions has gotten longer.     We can not make any conclusions using this confidence interval.Because the interval contains only negative numbers, we can say that the interval length between eruptions has gotten longer.

The chance that any jug of milk in the grocery store will be sour is 5%. Suppose you purchase 20 jugs of milk for the summer camp where you work. What is the expected number of jugs of sour milk in your purchase

In what exact scenarios would the "null hypothesis" be either rejected or accepted?
What exactly does it mean?

Is smoking during pregnancy associated with premature births? To investigate this question, researchers selected a random sample of 111 pregnant women who were smokers. The average pregnancy length for this sample of smokers was 262 days. From a large body of research, it is known that length of human pregnancy has a standard deviation of 16 days. The researchers assume that smoking does not affect the variability in pregnancy length. Find the 99% confidence interval to estimate the length of pregnancy for women who smoke. (Note: The critical $z$-value to use, $z_c$, is: 2.576) ( , ) Your answer should be rounded to 3 decimal places.

In Clinical trials of Liptor, 94 subjects were treated with Lipitor and 270 subjects were given the placebo. Among those treated with Lipitor, 7 developed infections. Among those given a placebo, 27 developed infections. We want to use a 0.05 significance level to test the claim that the rate of infections was the same for those treated with Lipitor and those given the placebo.

a) test claim using a hypothesis test

c) based on results is the rate of infection different for those treated with Lipitor?

Please do it out with the equation below. I am trying to understand it by hand rather than excel or SPSS first.

--> This is the equation i used. I got Z = -9.72 but i don't believe its right.

Consider the t-distribution with 18 degrees of freedom. Use Table D to find the proportion of this distribution that lies below

t=−1.33

Then use excel to confirm your result. Give your answer to two decimal places.

P(t < −1.33) =

In order to evaluate the effectiveness of a new type of plant food that was developed for tomatoes, a study was conducted in which a random sample of n = 68 plants received a certain amount of this new type of plant food each week for 14 weeks. The variable of interest is the number of tomatoes produced by each plant in the sample. The table below reports the descriptive statistics for this study:

Assuming the population is normally distributed, the investigators would like to construct a 98% confidence interval for the average number of tomatoes that all plants of this variety can produce when fed this supplement like this.
a) The margin of error is:  (3 decimals)

b) The corresponding 98% confidence interval for the true population mean is:
Lower Limit:  (3 decimals)
to
Upper Limit:  (3 decimals)
c) What would we conclude at α = 0.02 for the hypothesis test H₀: μ = 64.875 vs. H_a: μ ≠ 64.875?

We do not have enough evidence to conclude the true mean is 64.875.We have insufficient evidence to conclude the true mean is different from 64.875.    We do not have enough evidence to conclude the true mean is 60.00.We have enough evidence to conclude that the true mean is 64.875.We have sufficient evidence to conclude that the true mean is different from 64.875.

The following sample data have been collected from a paired sample from two populations. The claim is that the first population mean will be at least as large as the mean of the second population. This claim will be assumed to be true unless the data strongly suggest otherwise.

Population Data

1. State the appropriate null and alternative hypotheses.
2. Based on the sample data, what should you conclude about the null hypothesis? Test using α = 0.10.

Cholesterol is a fatty substance that is an important part of the outer lining (membrane) of cells in the body of animals. Its normal range for an adult is 120–240 mg/dl. The Food and Nutrition Institute of the Philippines found that the total cholesterol level for Filipino adults has a mean of 159.2 mg/dl and 84.1% of adults have a cholesterol level less than 200 mg/dl (http://www.fnri.dost.gov.ph/). Suppose that the total cholesterol level is normally distributed. (a) Determine the standard deviation of this distribution. (b) What are the quartiles (the 25% and 75% percentiles) of this distribution? (c) What is the value of the cholesterol level that exceeds 90% of the population? (d) An adult is at moderate risk if cholesterol level is more than one but less than two standard deviations above the mean. What percentage of the population is at moderate risk according to this criterion? (e) An adult whose cholesterol level is more than two standard deviations above the mean is thought to be at high risk. What percentage of the population is at high risk? (f) An adult whose cholesterol level is less than one standard deviations below the mean is thought to be at low risk. What percentage of the population is at low risk?

The table below gives the average high temperatures in January and July for 12 random cities in a region with 192 192 cities. Write a 99 99​% confidence interval for the mean temperature difference between summer and winter in the region.

Mean High Temperatures ​( degrees °​F)

City A B C D E F G H I J K L

July 73 71 78 74 91 88 71 87 74 65 74 85

Jan. 35 37 40 37 56 53 39 45 46 43 19 36

The confidence interval is left parenthesis nothing comma nothing right parenthesis . , . ​(Round to one decimal place as​ needed.)