Suppose that insurance companies did a survey. They randomly surveyed 410 drivers and found that 350 claimed they always buckle up. We are interested in the population proportion of drivers who claim they always buckle up. note: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though. Which distribution should be used for the problem? (state distribution)

When assumptions of normality are violated, data are nominal or ordinal, or we do not wish to make assumptions about a specific distribution, what is the appropriate type of statistical test? a. Repeated b. Blinded control group c. Non-parametric d. Parametric

If a distribution of data follows a normal distribution, we would expect that the __________, and __________ are all equal.

According to​ Benford's Law, a variety of different data sets include numbers with leading​ (first) digits that follow the distribution shown in the table below. Test for​goodness-of-fit with​ Benford's Law.   Leading Digit 1 2 3 4 5 6 7 8 9 ​Benford's law: distribution of leading digits ​30.1% ​17.6% ​12.5% ​9.7% ​7.9% ​6.7% ​5.8% ​5.1% ​4.6%   When working for the Brooklyn District​ Attorney, investigator Robert Burton analyzed the leading digits of the amounts from 784 checks issued by seven suspect companies. The frequencies were found to be​ 0, 12,​ 0, 73,​ 482, 186,​ 8, 23, and​ 0, and those digits correspond to the leading digits of​ 1, 2,​ 3, 4,​ 5, 6,​ 7, 8, and​ 9, respectively. If the observed frequencies are substantially different from the frequencies expected with​ Benford's Law, the check amounts appear to result from fraud. Use a 0.05 significance level to test for​ goodness-of-fit with​ Benford's Law. What is the value…

Histograms of random sample data are often used as an indication of the shape of the underlying population distribution. The histograms on the next page are based on random samples of size 30,50 and 100 from the same population. a. Using the midpoint labels of the three histograms, what would you say about the estimated range of population data from smallest to largest? Does the bulk of the data seem to be between 8 and 12 all in three histograms?  b. The population distribution from which the samples were drawn is symmetric and mound shaped, with the top of the mound at 10,95% of the data between 8 and 12, and 99.7% of data between 7 and 13. How well does each histogram reflect these characteristics?

Please answer the question in the photo. Thank you!

please do  " for this study, we should use.... (second screenshot) and b & c

Test Prep. A GRE prep company claims that average score improvement of their students is equal to 90 points. We want to see if it is different than this. We randomly sample students for their average improvement. The data we collected are below. GRE scores are known to be normally distributed. Points 90.4 84 77 75.2 81.5 78.4 96.5 97.3 101.5 85.3 69.5 88.6 92.4 Evaluate the company's claim using a hypothesis test. You wish to test the following claim (Ha) at a significance level of a = 0.05. (a) Write the hypothesis for the test. O Ho: H= 90 Ha: p = 90 O H;: H = 90 Ha: p 90 O Ho: H = 85.969 Ha: p = 85.969 Ο H : μ- 85. 969 H3: p 85.969 (b) What is the p-value for this test (round to 4 decimal place) (c) Based on the sample data, we sould conclude that ... O There is enough evidence at the a = 0.05 level to say that the average improvement is not 90 points. O There is not enough evidence at the a = 0.05 level to say that the average improvement is not 90. Question Help: O Message…