Exam 9: Testing the Difference Between Two Means, Two Variances, and Two Proportions

In a test of the difference between the two means below, what should the test value be for a $t$ test? Sample 1 Sample 2 Sample mean 680 735 Sample variance 550 60 Sample size 10 11

What is the critical value for a two-tailed $F$ test with $\alpha = 0.10$ , when the sample size from which the variance for the numerator was obtained is 10 , and the sample size from which the denominator was obtained is 24 ?

When finding the test value for an $F$ test, the smaller of the two variances should be placed in the numerator.

A reporter bought hamburgers at randomly selected stores of two different restaurant chains, and had the number of Calories in each hamburger measured. Can the reporter conclude, at $\alpha = 0.05$ , that the hamburgers from the two chains have a different number of Calories? Chain A Chain B Sample size 7 8 Sample mean 280 315 Sample standard deviation 23 27

The following display from a TI-84 Plus calculator presents the results of a hypothesis test for the difference between two means. The sample sizes are $n _ { 1 } = 12$ and $n _ { 2 } = 13$ . Can you reject $H _ { 0 }$ rejected at the $\alpha = 0.01$ level?

The formula used in the $z$ test for comparing the means from two independent populations is_______

A running coach wanted to see whether runners ran faster after eating spaghetti the night before. A group of six runners was randomly chosen for this study. Each ran a 5 kilometer race after having a normal dinner the night before, and then a week later, reran the same race after having a spaghetti dinner the night before. The times for their races are shown in the table below. What test value should be used in a $t$ test for these depende samples? Runner 1 Runner 2 Runner 3 Runner 4 Runner 5 Runner Regular Dinner 989 974 998 959 1005 985 Spaghetti Dinner 982 969 995 958 1006 988

$\text { In the } F \text { distribution, values of } F \text { cannot be negative, because variances are always }$ positive or zero.

64% of students at a university live on campus. A random sample found that 28 of 45 male students and 39 of 50 of female students live on campus. At the 0.05 level of Significance, is there sufficient evidence to support the claim that a difference exists Between the proportions of male and female students who live on campus?

The number of calories in a 12 -ounce serving of randomly-selected regular and lite beers is listed. Is there sufficient evidence to conclude that the mean number of calories for lite beers is significantly less than that for the regular beers? Use $\alpha = 0.10$ . Assume the variables are approximately normally distributed. Regular: 136 121 128 90 141 149 119 138 132 120 112 172 133 Lite: 100 110 105 103 115 99 123 137 121 156 a.State the hypotheses. b. Find the critical value(s). c. Compute the test value. d. Make the decision. e. Summarize the results.

A local charity believes they receive more money from people in the River Heights neighborhood than from people in the Lakeview neighborhood. They conducted a survey of 24 people randomly selected form each neighborhood and recorded the results. At $\alpha = 0.01$ , is their hypothesis correct? River Heights Lakeview =\ 35 /person =\ 25/ person =\ 5/ person =\ 8/ person =24 =24

Samples are independent when they are not related.

The following display from a TI-84 Plus calculator presents the results of a hypothesis test for the difference between two means. The sample sizes are $n _ { 1 } = 9$ and $n _ { 2 } = 12$ . What is the $P$ -value?

If the test value for the difference between the means of two large samples is $2.57$ when the critical value is $1.96$ , what decision should be made?

The formula of the test value to be used in a t test for dependent samples is .

Given the variances of the two samples below, find the test value and the degrees of freedom that should be used in an $F$ test. Sample 1 Sample 2 Variance 7 11 Sample size 14 26

In an experiment to determine whether there is a systematic difference between the weigh obtained with two different mass balances, six specimens were weighed, in grams, on eac balance. The following data were obtained: Specimen 1 14.89 14.89 2 13.06 13.07 3 14.49 14.49 4 13.25 13.23 5 10.18 10.14 6 7.58 7.57 State the null and alternate hypotheses.

A amateur golfer wishes to determine if there is a difference between the drive distances of her two favorite drivers. (A driver is a specialized club for driving the golf ball down $r$ i She hits fourteen balls with driver A and 10 balls with driver B. The The drive distances ( for the trials are show below. Driver A 302 283 283 291 241 268 276 263 296 268 291 262 274 278 Driver B 247 313 246 208 261 283 237 245 224 249 Assume that the populations are approximately normal. Can you conclude that there is a difference in the mean drive distances for the two drivers? Use the $\alpha = 0.01$ level of significance.

In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Fourteen randomly selected plots of land were treated with fertilizer $A$ , and 10 randomly selected plots were treated with fertilizer $B$ . The The number of pounds of harvested fruit was measured from each plot. Following are the results. Fertilizer A 479 385 400 417 405 403 386 450 406 434 437 409 429 352 Fertilizer B 404 403 387 427 429 404 464 418 411 340 Assume that the populations are approximately normal. Can you conclude that there is a difference in the mean yields for the two types of fertilizer? Use the $\alpha = 0.05$ level of significance.