A professional employee in a large corporation receives an average of $μ = 41.7$ e-mails per day. An anti-spam protection program was installed in the company’s server, and one month later, a random sample of 45 employees showed that they were receiving an average of $x̄ = 36.2$ e-mails per day. Assume that $σ = 18.45$. Use a 5% level of significance to test whether there has been a change (either way) in the average number of emails received per day per employee.

a.) What is α? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?$α$ = ___$H₀: μ$ = ___$H₁: μ$ ___The test is a ___ test. b.) Identify the Sampling Distribution you will use. What…

A sports league introduced a video referee to review certain critical plays. However, the system has not been without its controversies. One particular unfortunate incident led to an outcry among fans. Nevertheless, a poll after this event found that 57% of fans were still in favor of the continued use of the video referee. Suppose the size of this sample was 300 people. Complete parts a and b.

(a) Estimate the true proportion of fans in favor of keeping the video referee using a 99% confidence interval. (b) What is the margin of error for this sample? Answer : Given : Sample proportion $(p\hat) = 0.57$ Sample size…

A manufacturer claims that the mean lifetime of its lithium battery is 1000 hours. A homeowner selects 40 batteries and finds the mean lifetime to be 990 hours with a standard deviation of 80 hours. Test the manufacturer’s claim. Use α=0.05.

Answer: Given Data : Hypothesized Population Mean $(\mu) =1000$ Sample Standard Deviation $(s)=80$ Sample Size $ (n)=40$ Sample Mean $(x\bar)=990$ Significance Level $(\alpha)=0.05$ The null and alternative hypothesis : $$H_0:\mu=1000$$ $$H_a:\mu!=1000$$ The test statistic : $$t = \frac{\overline{x} – \mu}{\frac{s}{\sqrt{n}}}…

The amount of weight a high school student carries in his or her bookbag follows a normal distribution with a standard deviation of σ = 2 pounds. Suppose a random sample of 20 bookbags produced a mean of 13 pounds. Construct a 95% confidence interval to estimate the mean bookbag weight for all high school students.

Given Data : Sample mean $(x\bar)=13$ Population standard deviation $(\sigma) = 2$ Sample size $(n) = 20$ Confidence interval level $(CI) =95%$ The level of significance: $$\alpha=1-0.95=0.05$$ The critical value: $$z_c=Z_\frac\alpha2=Z_\frac{0.05}2=1.96$$ The confidence interval: $$CI = \overline{x} \pm z_c \cdot…