PLS ANSWER THESE FOUR QUESTIONS THEY BASICALLY GO HAND AND HAND WITH EACH OTHER **Context for Problems #1 through #15:**The farmers at Olde Port Orchards grow several varieties of apples, including Royal Gala, Golden Delicious, Honey Crisp, Pink Lady, and Red Delicious. Patrons at the farm's various fall harvest festivals can select one apple on their way off the property as a takeaway treat. The management is curious whether the apple varieties are selected comparably by festival patrons. A simple random sample of recent selections by festival patrons was recorded as follows:| Royal Gala | Golden Delicious | Honey Crisp | Pink Lady | Red Delicious ||------------|------------------|-------------|-----------|---------------|| 46 | 54 | 50 | 32 | 68 |Make no assumptions about the underlying distribution. Test the claim at the 1% level of significance.---**Item #12:** Determine the critical value, rounded to the nearest thousandth.[Textbox for answer]---**Question 13:**For Problems #1 through #15, consider the following context (same as above).| Royal Gala | Golden Delicious | Honey Crisp | Pink Lady | Red Delicious ||------------|------------------|-------------|-----------|---------------|| 46 | 54 | 50 | 32 | 68 |Make no assumptions about the underlying distribution. Test the claim at the 1% level of significance.**Item #13:** Determine the *p*-value, rounded to the nearest ten-thousandth: 0.####[Textbox for answer] **Item #14:** What is the most appropriate technical conclusion, with any relevant qualifiers, based on the available evidence and testing at the indicated level of significance?- ○ highly reject the null hypothesis (extremely significant)- ○ reject the null hypothesis (significant)- ○ marginally reject the null hypothesis (marginally significant)- ○ highly fail to reject the null hypothesis (extremely insignificant)- ○ fail to reject the null hypothesis (insignificant)- ○ marginally fail to reject the null hypothesis (marginally insignificant)- ○ cannot draw any conclusion based on the available evidence- ○ no conclusion---**QUESTION 15***For Problems #1 through #15, consider the following context:* The farmers at Olde Port Orchards grow a number of varieties of apples, including Royal Gala, Golden Delicious, Honey Crisp, Pink Lady, and Red Delicious. Patrons at the farm's various fall harvest festivals can select one apple on their way off the property as a takeaway treat. The management wonders if the apple varieties are selected comparably by festival patrons. A simple random sample of recent selections by festival patrons was as follows:| Royal Gala | Golden Delicious | Honey Crisp | Pink Lady | Red Delicious ||------------|------------------|-------------|-----------|---------------|| 46 | 54 | 50 | 32 | 68 |Make no assumptions about the underlying distribution. Test the claim at the 1% level of significance.**Item #15:** What is the most appropriate contextual conclusion or interpretation, with any relevant qualifiers, based on the available evidence and testing at the indicated level of significance?- ○ It is highly reasonable to claim that the apples are selected comparably, a highly statistically uninteresting finding.- ○ It is reasonable to claim that the apples are selected comparably, a statistically uninteresting finding.- ○ It is marginally reasonable to claim that the apples are selected comparably, a marginally statistically uninteresting finding.- ○ It is highly unreasonable to claim that the apples are selected comparably, a highly statistically interesting finding.- ○ It is unreasonable to claim that the apples are selected comparably, a statistically interesting finding.- ○ It is marginally unreasonable to claim that the apples are selected comparably, a marginally statistically interesting finding.- ○ cannot provide any interpretations at this time based on the available evidence- ○ no conclusion

The categorical variable is Variety of apple. A sample of 5 observations is given. We have to find the critical value and write conclusion. This is Chi-Square test for goodness-of-fit.Apple Variety Observed Expected O - E (O - E)² / E Royal Gala 46 50.000 -4.000 0.320 Golden Delicious 54 50.000 4.000 0.320 Honey Crisp 50 50.000 0.000 0.000 Pink Lady 32 50.000 -18.000 6.480 Red Delicious 68 50.000 18.000 6.480 Total 250 250.000 0.000 13.600 The value of the test statistic is χ2= 13.600.Df = n-1 = 5-1 = 4 From Chi-Square distribution table, the critical value at 4 df and 1% level is 13.277. Critical value = 13.277.EXCEL command is “= CHIDIST (x, deg_freedom)” For p-value, enter in EXCEL as, “= CHIDIST (13.600, 4)” P-value = 0.0087.It is reasonably to claim that the apples are selected comparably, a statistically uninterested finding.