Listed below are time intervals​ (min) between eruptions of a geyser. Assume that the​ "recent" times are within the past few​ years, the​ "past" times are from around 20 years​ ago, and that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Does it appear that the mean time interval has​ changed? Is the conclusion affected by whether the significance level is 0.10 or 0.01​?   Recent 78 92 90 78 58 99 63 86 71 89 83 84 55 82 73 102 61   Past 90 87 93 94 63 84 86 92 86 91 89 91             Let μ1 be the recent times and let μ2 be the past times. What are the null and alternative​ hypotheses?     A. H0​: μ1≠μ2 H1​: μ1=μ2   B. H0​: μ1=μ2 H1​: μ1>μ2   C. H0​: μ1<μ2 H1​: μ1=μ2   D. H0​: μ1=μ2 H1​: μ1≠μ2 Calculate the test statistic.   t=nothing ​(Round to two decimal places as​ needed.) Find the​ P-value.   ​P-value=nothing ​(Round to three decimal places as​ needed.) Make a conclusion about the null hypothesis and a final conclusion that addresses the original claim. Use a significance level of 0.10.   ▼   Fail to reject Reject H0 because the​ P-value is ▼   less than or equal to greater than the significance level. There ▼   is is not sufficient evidence that the mean time interval has changed. Is the conclusion affected by whether the significance level is 0.10 or 0.01​?     A. ​No, the conclusion is not affected by the significance level because H0 is rejected regardless of whether a significance level of 0.10 or 0.01 is used.   B. ​No, the conclusion is not affected by the significance level because H0 is not rejected regardless of whether a significance level of 0.10 or 0.01 is used.   C. ​Yes, the conclusion is affected by the significance level because H0 is rejected when the significance level is 0.10 but is not rejected when the significance level is 0.01.   D. ​Yes, the conclusion is affected by the significance level because H0 is rejected when the significance level is 0.01 but is not rejected when the significance level is 0.10.

The adult eastern hellbender (a type of giant salamander) has a length which is normally distributed with a mean of 31.8 cm and a standard deviation of 2.7 cm, while the adult Ozark hellbender has a length which is normally distributed with a mean of 34.9 and a standard deviation of 4.5. Random samples of a size 100 are selected of each species of hellbender. The box plots are created for each dataset. Which box plot will most likely have the larger interquartile range? O a. The IQR will be around the same for each. 0. O b. Either is equally likely to be larger than the other. 0 O c. The Ozark hellbenders. 0 O d. The eastern hellbenders. 0

Let's assume that the distribution of gas on a given day in a town is normally distributed with mean of $4.3371 with a standard deviation of $0.4192. What proportion of gas stations are charging less than $3.4387? 98.3949% 0.8026% 1.6051% 3.2103% O 0%

Suppose x has a distribution with a mean of 13.9 and a standard deviation of 2.1. Random samples of size n=49 are drawn. What would be the mean and standard deviation of the x̄ distribution?

When samples of size 30 are collected from a normal population that has a mean of 200 and a standard deviation of 40, the standard deviation of the sampling distribution is?

A triathlon consisting of swimming, cycling, and running is one of the more strenuous amateur sporting events. An article reports on a research study involving nine male triathletes. Maximum heart rate (beats/min) was recorded during performance of each of the three events. For swimming, the sample mean and sample standard deviation were 187.0 and 7.2, respectively. Assuming that the heart-rate distribution is (approximately) normal, construct a 98% CI for true mean heart rate of triathletes while swimming. (Round your answers to one decimal place.) USE SALT beats/min You may need to use the appropriate table in the Appendix of Tables to answer this question.

A population has a mean μ=40 and a standard deviation σ=4. What is the standard deviation of the sampling distribution of the sample means if the sample size is n=16?

Suppose a certain population of observations follows a bell-shaped distribution. Based on the 68/95/99.7 rule, what percentage of the data in the population are between three standard deviations below the mean and one standard deviation above the mean?

Suppose that in 2020 the average song length is 245 seconds, with a standard deviation of 28 seconds. what is the approximate standard error for the sampling distribution of mean song lengths due samples size of 64 A. 28.0 B. 2.3 C. 7.0 d. 3.5

In a study of birth order and intelligence, IQ tests were given to 18- and 19-year-old men to estimate the size of the difference, if any, between the mean IQs of firstborn sons and secondborn sons. The following data for 10 firstborn sons and 10 secondborn sons are consistent with the means and standard deviations reported in the article. It is reasonable to assume that the samples come from populations that are approximately normal. Can you conclude that the mean IQ of firstborn sons is greater than the mean IQ of secondborn sons? Let μ1 denote the mean IQ of firstborn sons and μ2 denote the mean IQ of secondborn sons. Use the α = 0.01 level and the P-value method with the table. Firstborn 128 101 128 112 121 105 122 98 106 108 Secondborn 121 125 110 107 114 93 80 94 91 83 Part(a): State the appropriate null and alternate hypotheses. H0:   H1: This is a _____…