Berdasarkan pembahasan maka diperoleh kesimpulan:

• conclude that there is a significant difference in the means of teacher salaries between Massachusetts and New York (Bahwa ada perbedaan yang signifikan antara gaji guru massachusetts dan new york.)

Teknik simple random sampling dibagi dari 4 kata yaitu teknik, simple, random, sampling. Teknik memilik arti suatu cara/tatanan/skil, simple adalah sederhana sesuai terjemahan inggris ke indonesianya, random yang berati terjemahan indonesia yaitu acak, sampling adalah sampel.

Penjelasan dengan langkah-langkah:

Based on the information provided, we can conduct a hypothesis test to determine if there is a significant difference in the means of teacher salaries between Massachusetts and New York.

• Null hypothesis (H0): There is no significant difference in the means of teacher salaries between Massachusetts and New York.
• Alternative hypothesis (H1): There is a significant difference in the means of teacher salaries between Massachusetts and New York.

To conduct the hypothesis test, we can use a two-sample t-test, since we have two independent samples and the population standard deviations are not known. The test statistic is calculated as:

t = (x1 - x2) / sqrt[(s1^2/n1) + (s2^2/n2)]

where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

Using the information given in the problem, we can calculate the test statistic as follows:

• t = (73,195 - 76,409) / sqrt[(7,800^2/45) + (8,200^2/45)]
• t = -3.214

The degrees of freedom for the test are (n1 + n2 - 2) = 88 (rounded down from 89). At a significance level of α = 0.10 and with 88 degrees of freedom, the critical value for a two-tailed test is ±1.645.

Since the calculated test statistic (t = -3.214) falls outside the critical region (±1.645), we can reject the null hypothesis. This means that there is sufficient evidence to suggest that there is a significant difference in the means of teacher salaries between Massachusetts and New York.

Alternatively, we can calculate the p-value for the test statistic. The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming that the null hypothesis is true. Using a t-distribution table or calculator, we can find that the p-value for a two-tailed test with 88 degrees of freedom and a test statistic of -3.214 is approximately 0.002.

Since the p-value (0.002) is less than the significance level of α = 0.10, we can reject the null hypothesis and conclude that there is a significant difference in the means of teacher salaries between Massachusetts and New York.

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