A food manufacturer claims that eating its new cereal as part of a daily diet lowers total blood cholesterol levels. The table shows the total blood cholesterol levels​ (in milligrams per deciliter of​ blood) of seven patients before eating the cereal and after one year of eating the cereal as part of their diets. Use technology to test the mean difference. Assume the samples are random and​ dependent, and the population is normally distributed. At α=0.05​, can you conclude that the new cereal lowers total blood cholesterol​ levels? Patient 1 2 3 4 5 6 7   Total Blood Cholesterol (Before) 205 230 235 235 240 270 230   Total Blood Cholesterol​ (After) 197 225 239 231 235 269 228         Let the blood cholesterol level before eating the cereal be population 1. Let the blood cholesterol level after eating the cereal be population 2. Identify the null and alternative​ hypotheses, where μd=μ1−μ2. Choose the correct answer below.     A. H0​: μd≤0 HA​: μd>0   B. H0​: μd=0 HA​: μd≠0   C. H0​: μd≠0 HA​: μd=0   D. H0​: μd≥0 HA​: μd<0 Calculate the standardized test statistic.   t=nothing ​(Round to three decimal places as​ needed.) Calculate the​ P-value.   ​P-value=nothing ​(Round to four decimal places as​ needed.) State the conclusion.   ▼   Reject Fail to reject H0. There ▼   is is not sufficient evidence to support the claim that the new cereal lowers total blood cholesterol levels.

Consider a normal population with µ = 50 and σ = 6. A sample size of at least which size needs to be obtained in order to achieve a standard error of σM = 2 or less?

The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 11.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight full-time faculty for one week is shown in the table below. At a =0.10, can you reject the dean's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 12.4 8.7 12.3 6.9 5.4 10.4 14.8 8.70 (a) Write the claim mathematically and identify H, and H. Which of the following correctly states H, and H ? O A. Ho: us11.0 O B. Ho: H#11.0 OC. Ho: H>11.0 Ha>11.0 Ha: u =11.0 Hai HS11.0 OD. Ho: H<11.0 O E. Ho:µ211.0 OF. Ho:H=11.0 Hgi µ#11.0 Ha: 211.0 Hai H<11.0 (b) Use technology to find the P-value. P= (Round to three decimal places as needed.) Click to select your answer(s). (? P Type here to search a 7:16 PM (? 4/25/2021 14 I01 10 f8 fo AA insert prt sc delete %24 4. %23 & 6. 8. 9- - backspace hom

An engineer wants to know if producing metal bars using a new experimental treatment rather than the conventional treatment makes a difference in the tensile strength of the bars (the ability to resist tearing when pulled lengthwise). At a = 0.20, answer. Assume the population variances are equal and the samples are random. If convenient, use technology to solve the problem. Treatment Tensile strengths (newtons per square milimeter) Experimental 392 355 448 363 400 425 353 Conventional 445 377 428 355 363 358 382 408 390 373 Identify the claim and state Ho and Ha. The claim is "The new treatment V in the tensile strength of the bars." What are Ho and H,? The null hypothesis, Hg, is V. The alternative hypothesis, Hg. is Which hypothesis is the claim? O The null hypothesis, Hg The altemative hypothesis, Ha Decide whether to reject or fail to reject the null hypothesis. V the null hypothesis. Interpret the decision in the context of the original claim. At the 20% significance level,…

An employment information service claims the mean annual salary for senior level product engineers is ​$97,000. The annual salaries​ (in dollars) for a random sample of 16 senior level product engineers are shown in the table to the right. At α=0.01​, test the claim that the mean salary is ​$97,000. Complete parts​ (a) through​ (e) below. Assume the population is normally distributed.        Annual Salaries  100 ​,687 96 ​,268 93 ​,513 112 ​,821   82 ​,514 74 ​,155 77 ​,080 81 ​,002 102 ​,392 76 ​,182 104 ​,074 103 ​,923 91 ​,069 82 ​,156 85 ​,068 110 ​,297         Question content area bottom Part 1 ​(a) Identify the claim and state H0 and Ha.   H0:  muμ   equals=   9700097000 Ha:  muμ   not equals≠   9700097000 ​(Type integers or decimals. Do not​ round.)   The claim is the null   hypothesis. Part 2 ​(b) Use…

Assume that the data values in this problem come from independent populations and that each population follows a normal distribution.Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year, many small plots of equal size but different soil/fertilizer conditions are planted with wheat. At the end of the growing season, the yield (in pounds) of the wheat on the plot is measured. For a random sample of years, one plot gave the following annual wheat production (in pounds).4.14    4.24    4.24    3.58    3.55    3.82    4.08    4.37    3.92    3.82    4.17    3.10    4.89    2.93    4.98    3.34Use a calculator to verify that, for this plot, the sample variance is s2 ≈ 0.3238.

The lifetime X of a certain electronic component in hours is an exponential random variable with a mean of 4.3. Determine the variance of X. The answer should be a number rounded to five decimal places,

A food manufacturer claims that eating its new cereal as part of a daily diet lowers total blood cholesterol levels. The table shows the total blood cholesterol levels (in milligrams per deciliter of blood) of seven patients before eating the cereal and after one year of eating the cereal as part of their diets. Use technology to test the mean difference. Assume the samples are random and dependent, and the population is normally distributed. At α = 0.05, can you conclude that the new cereal lowers total blood cholesterol levels? Patient 1 2 3 4 5 6 7 Total Blood Cholesterol (Before) 205 220 240 235 250 270 230 Total Blood Cholesterol (After) 196 217 242 232 245 267 225 Let the blood cholesterol level before eating the cereal be population 1. Let the blood cholesterol level after eating the cereal be population 2. Identify the null and alternative hypotheses, where μμ₁ −μ₂. Choose the correct answer below. A. Ho: Hd #0 HA: Hd=0 B. Ho: Hd ≤0 HA: Md>0 C. Ho: Hd = 0 HA: Md #0 D. Ho: Hd 20…

Ria wants to know if there is a significant difference between the average monthly hair growth using Shampoo A vs Shampoo B. She recruited eight participants and compared their average monthly hair growth (in centimeters) using the two different brands. Her data is assumed to be normally distributed which produced the following values: Shampoo A 0.50 1.00 1.50 1.70 0.75 0.60 1.25 1.25 Shampoo B 1.00 1.25 2.00 2.00 1.50 1.00 1.50 1.75 Choose the appropriate test statistic and make a conclusion about the problem. Show your output below in a step-by-step manner: 21 - 22. State the null and alternative hypotheses. 23- 48. Make a decision about the null hypothesis: (23 - 26) Calculate the degree of freedom (27.) Assume that a 05 (two-tailed). Identify the critical values and state a decision rule.

Test the hypothesis that the average content of containers of a particular lubricant is 10 L if the contents of a random sample of 10 containers are 10.2, 9.7, 10.1, 10.3, 10.1, 9.8, 9.9, 10.4, 10.3, and 9.8 liters. Use a 0.01 level of significance and assume the distribution of contents is normal.