Question

For the problems on the NEXT page you must conduct a complete hypothesis test procedure for these problems making it clear what formula was being used. Be sure to formulate both hypotheses, identify critical values and rejection regions where appropriate, your test statistic, as well as stating your final conclusion IN NONTECHNICAL TERMS (Translation Assume you are stating your conclusion to somebody with no knowledge of statistics.)!! A simple random sample of birth weights of 30 girls has a standard deviation of 829.5 hg. Use a 0.01 significance level to test the claim that birth weights of girls have the same standard deviation as birth weights of boys, which is 660.2 hg. It is safe to assume birth weights have a bell-shaped distribution 6. 7. A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 306 randomly selected people over the age of 55, 68 dream in black and white. Among 298 randomly selected people under the age of 25, 13 dream in black and white. Use a 0.01 significance level to test the claim that people over the age of 55 dream in black and white at a greater rate than those under the age of 25

Please solve both questions. Instructions are at the top

Answer 1

Solution:-

6)

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

Null hypothesis H₀: σ = 660.2

Alternative hypothesis H_A: σ $\neq$ 660.2

Formulate an analysis plan. For this analysis, the significance level is 0.01.

Analyze sample data. Using sample data, the degrees of freedom (DF), and the test statistic (X²).

DF = n - 1 = 30 -1

D.F = 29

$\chi ^{2}=\frac{(n-1)s^{2}}{\sigma ^{2}_{0}}$

$\chi ^{2}=\frac{(30-1)\times (829.5)^{2}} {(660.2)^2}$

$\chi ^{2}= 45.78$

Χ²_Critical = 49.59

Rejection region is Χ²_Critical > 49.59

Interpret results. Since the Χ²-value does not lies in the rejection region, hence we failed to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that birth weights of girls have the same standard deviation as birth weights of boys, which is 660.2 hg.