Sales Price ($) City Miami McKinney Newberg 100 1.30 90 1.60 90 1.80 40 2.00 Prescott 38 Tacoma San Jose 2.40 32 2.90 2. Assume that a researcher is interested in finding out the relationship between standardized test scores and household income. Seven participants have been randomly selected and their ACT Composite score and household income are reported. By performing a test, can you conclude that there is a significant relationship between household income and ACT Composite score? State your null and alternative hypotheses. Please show all of the required steps. Use the data in the table below. Assume a = .05 points АСT Income (in thousands) Composite Score 16 30 18 21 18 24 21 59 23 55 25 105 26 35

Let r denote the linear correlation between income (x) and ACT composite score (y). The hypotheses are given below:

Null hypothesis:

H₀: r = 0

That is, the sample correlation coefficient (r) is not significantly different from zero. There is no significant positive linear relationship between income and ACT composite score.

Alternative hypothesis:

H_a: r ≠ 0

That is, the sample correlation coefficient is significantly different from zero.

There is a significant positive linear relationship between income and ACT composite score.

Degrees of freedom:

The formula for degrees of freedom is as follows:

Df = n – 2.

The number of data values given are 7, that is n = 7.

Substitute n = 7 in the degrees of freedom formula.

Df = n – 2 = 10 – 2 = 8.

The level of significance for the test is 0.05.

Sample correlation coefficient:

The value of the sample correlation coefficient (r) can be obtained using Excel formula.

Enter the values of income in columns A2:A8 in Excel.

Enter the values of ACT composite score in columns B2:B8 in Excel.

Enter the function, =CORREL(A2:A8,B2:B8).

Thus, the value of the sample correlation coefficient, r is 0.6203.

Test Statistic:

The test statistic for hypothesis test is calculated as follows: