A national internet service provider (ISP) claims that its broadband internet download speed is 275 megabits per second (Mbps) on average. To the contrary, there have recently been widespread reports that consumers are experiencing much slower download speeds from this ISP. An organization organization decided to investigate the issue. They took a random sample of 18 internet speeds from around the nation. The observations are given below.

286 245 285 293 298 303 226 262 283

267 229 269 249 257 284 274 302 290

Using alpha = 0.1, test the hypothesis that the average download speed is 275 Mbps, as advertised by the ISP. Assume that the distribution of all broadband internet measurements from this ISP is approximately distributed. Use the critical value method.

State the null alternative hypothesis for this test.

Ho:? =------

H1:? =------

Determine if this test left-tailed, right-tailed, or two-tailed.

Should the standard normal (z) distribution or student's (t) distribution be used for this test?

- Determine the critical value (s) for this hypothesis test. Round the solution (s) to four decimal places. If more than one critical value exists, enter the solutions using a comma-separated list.

=------

Determine the test statistic. round the solution to four decimal places.

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Determine the appropriate conclusion for this hypothesis test.

- The sample data do not provide evidence to reject the null hypothesis that the mean download speed from this ISP is 275 Mbps and thus we conclude that it is likely the average download speed from this ISP 275 Mbps, as advertised.

- The sample data do not provide sufficient evidence to reject the alternative hypothesis that the mean download speed from this ISP is less than 275 and thus we conclude that the mean download speed from this ISP is likely less than 275 Mbps on average.

- The sample data provide sufficient evidence to reject the null hypothesis that the mean download speed from this ISP is 275 Mbps and thus we conclude that that is likely the true average download speed from this ISP less than advertised.

- The sample data provide sufficient evidence to reject the alternative hypothesis that the mean download speed from this ISP is less than 275 and thus we conclude that the mean download speed from this ISP is likely 275 Mbps on average.

2- Determine the critical value (s) for a two-tailed hypothesis test for a mean with the given characteristics. Round any z-value solution to two decimal places. round any t--value solution to four decimal places.

The significance level of the test is 5%

the sample size is 34

the population standard deviation is known to be 2.3

The standard normal (z) distribution should be used.

The critical value (s) for the test are given by z =

3- Determine the critical value for a left-tailed hypothesis test for a mean with the characteristics. Round any z-value solution to two decimal places. Round any t-value solution to four decimal places.

Alpha = 0.005

The sample size is 40

The population standard deviation is not known.

The student's t distribution should be used.

The critical value (s) for the test are given by t =------

4- A politician recently claimed the 47% of Americans support legalized marijuana. A political scientist thinks that the percentage of Americans that support legalized marijuana is actually much higher. She plans to collect data to determine if the percentage is indeed higher than what is claimed by the politician.

Determine the null and alternative hypothesis for the above hypothesis test.,

Ho:p > 0.47, H1:p = 0.47

Ho:p = 0.47, H1:p < 0.47

Ho:p = 0.47, H1:p > 0.47

Ho:p < 0.47, H1:p > 0.47

5- An epidemiologist with the Florida department of health needs to estimate the proportion of Floridians who are infected with the corona virus but are asymptomatic (show no signs of the virus). The epidemiologist compiled a preliminary random sample of infected patients and found that 47% of the sample were also asymptomatic.

How large a sample should be selected such that the margin of error of the estimate for a 95% confidence interval is at most 1.87%. Round the solution up to the nearest whole number.