Question

State	Student population	Undergraduate students	Tuition($)
CA	14125	14125	$9,761.00
CA	22370	21351	$19,002.00
CA	26053	24319	$12,634.00
CA	1090	1050	$14,599.00
CA	10131	8814	$6,794.00
CA	7455	7054	$14,834.00
CA	17875	16710	$14,185.00
CA	16219	13278	$4,957.00
CA	16538	13474	$11,425.00
CA	25325	22261	$5,879.00
CA	40905	35162	$8,562.00
CA	37622	31566	$9,654.00
CA	28531	24818	$3,907.00
CA	7584	6764	$11,233.00
CA	41319	35839	$5,958.00
CA	31255	28454	$9,841.00
CA	20692	18327	$8,704.00
CA	15755	14615	$10,454.00
CA	10327	9057	$6,768.00
CA	2151	2151	$11,088.00
CA	15697	15697	$7,481.00
CA	8525	7862	$14,140.00
CA	19948	19948	$6,406.00
CA	23532	23532	$7,543.00
CA	35158	30272	$13,363.00
CA	29758	26680	$13,551.00
CA	35835	27778	$13,906.00
CA	28083	28083	$6,931.00
CA	9481	8667	$16,807.00
CA	41891	30574	$18,178.00
CA	37380	30066	$16,446.00
CA	35242	29307	$13,944.00
CA	44027	31002	$14,760.00
CA	7967	7375	$13,147.00
CA	23279	20073	$12,404.00
CA	35772	28587	$14,616.00
CA	25057	22186	$16,154.00
CA	19457	17577	$16,792.00
NV	33914	33914	$7,488.00
NV	3244	3244	$12,230.00
NV	4216	4216	$15,136.00
NV	30471	25279	$11,582.00
NV	21657	18348	$16,230.00
NV	3642	3642	$11,361.00
OR	3016	2737	$14,777.00
OR	5486	5380	$16,503.00
OR	30896	25838	$19,205.00
OR	26693	21167	$13,573.00
OR	6191	5523	$9,924.00
OR	22887	19340	$15,100.00
OR	5336	4759	$15,898.00
WA	13322	13322	$7,337.00
WA	3425	3425	$7,657.00
WA	12901	12080	$14,124.00
WA	3122	3122	$7,617.00
WA	10000	10000	$7,483.00
WA	3883	3883	$5,042.00
WA	6708	6708	$8,034.00
WA	12607	11473	$11,393.00
WA	1971	1971	$6,558.00
WA	8048	8048	$9,229.00
WA	6824	6824	$8,704.00
WA	3697	3697	$6,544.00
WA	6259	6259	$3,317.00
WA	544	544	$8,679.00
WA	6476	6476	$5,453.00
WA	2094	2094	$6,658.00
WA	6048	6048	$5,976.00
WA	3763	3763	$6,396.00
WA	6928	6928	$4,546.00
WA	4670	4670	$7,937.00
WA	6716	6716	$8,433.00
WA	5589	5589	$6,528.00
WA	6496	6496	$5,959.00
WA	3907	3610	$12,407.00
WA	5981	5365	$7,536.00
WA	46166	31331	$9,443.00
WA	5162	4436	$8,674.00
WA	30614	25277	$17,885.00
WA	15915	14968	$16,117.00
WA	4007	4007	$7,262.00

Using hypothesis testing, determine whether the average tuition at public universities and colleges on the west is greater than the national average of $9,970 at the 5% significance level.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u < 9970
Alternative hypothesis: u > 9970

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 454.588
DF = n - 1

D.F = 80
t = (x - u) / SE

t = 1.553

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of 1.553.

Thus the P-value in this analysis is 0.062.

Interpret results. Since the P-value (0.062) is greater than the significance level (0.05), we cannot reject the null hypothesis.

From the above test we do not have sufficient evidence in the favor of the claim that the average tuition at public universities and colleges on the west is greater than the national average of $9,970 at the 5% significance level.