IQ test scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the IQ score that corresponds to a z-score of 1.96.

A sports scientist tests a new warm-up routine to see if it slows down 40-yard sprint times. H₀: The average sprint time with the new routine is equal to 4.5 seconds. H₁: The average sprint time with the new routine is greater than 4.5 seconds. α = 0.01 p-value = 0.04 Fill in the blanks: At the 1% significance level, the scientist should [blank] the null hypothesis. The scientist has evidence that the new routine [conclusion] slows down 40-yard sprint times.

We have evidence to support the claim.

Assume that the random variable X is normally distributed, with mean

In a recent survey, 65% of park visitors supported adding more hiking trails in the local nature reserve. If 20 visitors are selected at random, what is the mean number who would support adding more trails?

A factory produces light bulbs, and their quality control department claims that the average lifespan of their bulbs is at least 1,000 hours. You are tasked with checking if the average lifespan is less than 1,000 hours. Is this a left-tailed, right-tailed, or two-tailed test? 

Find the variance of the binomial distribution for which n = 110 and p = 0.5.

A marketing campaign claims that it will increase the average number of website visitors per day by at least 10%. The company’s website currently gets 5,000 visitors per day. After the campaign, the average number of visitors increases to 5,500 per day. You want to test if the increase in visitors is greater than 5,000, which would indicate that the campaign has had a significant impact. Is this a left-tailed, right-tailed, or two-tailed test? 

Identify the data set’s level of measurement. Type of climbing: Trad, Sport, Alpine, Bouldering, Ice

A university claims that the average SAT score of its incoming students is at least 1200. A concerned student group believes that the average SAT score is actually less than 1200. You randomly select 50 students and find that the average SAT score is 1180 with a standard deviation of 100. You want to test whether the average SAT score is significantly less than the claimed 1200. Is this a left-tailed, right-tailed, or two-tailed test?